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#1
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Two Cap Puzzle
John Larkin wrote:
On Sat, 17 Jul 2010 02:42:20 -0400, ehsjr wrote: Paul Hovnanian P.E. wrote: My solution for the missing energy. But John's puzzle stated that energy *is* conserved, so there is no missing energy in his puzzle. He said _charge_ was not conserved, in some cases. Or maybe it's a different puzzle? What I recall was a 4F cap that was charged to .5 volts, therefore Q=2 coulombs. He magically cut in half. (I don't know why he didn't start with 2 caps, 2F each, in parallel.) The resultant 2F caps each retained the .5V charge for Q=1 coulomb per cap. He then puts them in series resulting in *a 1F cap charged to 1 volt* which is Q=1 coulomb, and claims there's 1 coulomb missing. That's the fallacy. The result is NOT a 1F cap. The result is 2 2F caps, in series. Each cap has Q=1 coulomb - there is no missing coulomb. Doesn't matter that total circuit C = 1 F. Ed But every 1F cap is, internally, two 2F caps in series. Just draw a dotted line midway through the dielectric. Play that game all you want. That "game" leads nowhere. It implies that all capacitors are internally a series string of infinitely small (physical) capacitors and infinitely large capacitance for each. This all reminds me of the 3 men rent a hotel room puzzle. The clerk tells them it will be 30 dollars, so each hands him a 10 dollar bill. Later, the clerk realizes he's made an error, the rate is only $25. So he gives 5 ones to the bellhop & instructs him to give the money back to the men. The bellhop can't divide it equally, so he goes to their room and hands each man a dollar, and pockets the other 2 bucks. Now, each man has gotten a dollar back, so each has given a total of $9 to the clerk. That's $27, and the bellhop has 2 bucks in his pocket. Where is the other dollar? After the two 1F caps are separated and rearranged in series, if you discharge them through a resistor, you will recover 1 coulomb. My point all along is that, in actual circuit design, the generalism "charge is conserved" is dangerous, given that "charge" is ampere-seconds that you can actually measure and use. Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. Ed John |
#2
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Two Cap Puzzle
On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr
wrote: John Larkin wrote: On Sat, 17 Jul 2010 02:42:20 -0400, ehsjr wrote: Paul Hovnanian P.E. wrote: My solution for the missing energy. But John's puzzle stated that energy *is* conserved, so there is no missing energy in his puzzle. He said _charge_ was not conserved, in some cases. Or maybe it's a different puzzle? What I recall was a 4F cap that was charged to .5 volts, therefore Q=2 coulombs. He magically cut in half. (I don't know why he didn't start with 2 caps, 2F each, in parallel.) The resultant 2F caps each retained the .5V charge for Q=1 coulomb per cap. He then puts them in series resulting in *a 1F cap charged to 1 volt* which is Q=1 coulomb, and claims there's 1 coulomb missing. That's the fallacy. The result is NOT a 1F cap. The result is 2 2F caps, in series. Each cap has Q=1 coulomb - there is no missing coulomb. Doesn't matter that total circuit C = 1 F. Ed But every 1F cap is, internally, two 2F caps in series. Just draw a dotted line midway through the dielectric. Play that game all you want. That "game" leads nowhere. It implies that all capacitors are internally a series string of infinitely small (physical) capacitors and infinitely large capacitance for each. This all reminds me of the 3 men rent a hotel room puzzle. The clerk tells them it will be 30 dollars, so each hands him a 10 dollar bill. Later, the clerk realizes he's made an error, the rate is only $25. So he gives 5 ones to the bellhop & instructs him to give the money back to the men. The bellhop can't divide it equally, so he goes to their room and hands each man a dollar, and pockets the other 2 bucks. Now, each man has gotten a dollar back, so each has given a total of $9 to the clerk. That's $27, and the bellhop has 2 bucks in his pocket. Where is the other dollar? After the two 1F caps are separated and rearranged in series, if you discharge them through a resistor, you will recover 1 coulomb. My point all along is that, in actual circuit design, the generalism "charge is conserved" is dangerous, given that "charge" is ampere-seconds that you can actually measure and use. Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. Ed John John "The Bloviator" Larkin obfuscates the obvious. There is no inconsistency. There is no magic. TINSTAAFL! ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | Spice is like a sports car... Only as good as the person behind the wheel. |
#3
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Two Cap Puzzle
On Wed, 21 Jul 2010 20:02:50 -0700, Jim Thompson wrote:
On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr wrote: John Larkin wrote: On Sat, 17 Jul 2010 02:42:20 -0400, ehsjr wrote: Paul Hovnanian P.E. wrote: My solution for the missing energy. But John's puzzle stated that energy *is* conserved, so there is no missing energy in his puzzle. He said _charge_ was not conserved, in some cases. Or maybe it's a different puzzle? What I recall was a 4F cap that was charged to .5 volts, therefore Q=2 coulombs. He magically cut in half. (I don't know why he didn't start with 2 caps, 2F each, in parallel.) The resultant 2F caps each retained the .5V charge for Q=1 coulomb per cap. He then puts them in series resulting in *a 1F cap charged to 1 volt* which is Q=1 coulomb, and claims there's 1 coulomb missing. That's the fallacy. The result is NOT a 1F cap. The result is 2 2F caps, in series. Each cap has Q=1 coulomb - there is no missing coulomb. Doesn't matter that total circuit C = 1 F. Ed But every 1F cap is, internally, two 2F caps in series. Just draw a dotted line midway through the dielectric. Play that game all you want. That "game" leads nowhere. It implies that all capacitors are internally a series string of infinitely small (physical) capacitors and infinitely large capacitance for each. This all reminds me of the 3 men rent a hotel room puzzle. The clerk tells them it will be 30 dollars, so each hands him a 10 dollar bill. Later, the clerk realizes he's made an error, the rate is only $25. So he gives 5 ones to the bellhop & instructs him to give the money back to the men. The bellhop can't divide it equally, so he goes to their room and hands each man a dollar, and pockets the other 2 bucks. Now, each man has gotten a dollar back, so each has given a total of $9 to the clerk. That's $27, and the bellhop has 2 bucks in his pocket. Where is the other dollar? After the two 1F caps are separated and rearranged in series, if you discharge them through a resistor, you will recover 1 coulomb. My point all along is that, in actual circuit design, the generalism "charge is conserved" is dangerous, given that "charge" is ampere-seconds that you can actually measure and use. Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. Ed John John "The Bloviator" Larkin obfuscates the obvious. There is no inconsistency. There is no magic. TINSTAAFL! TANSTAAFL! 'Aint', not 'isn't' ) I've read Larry Niven too. Grant. ...Jim Thompson |
#4
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Two Cap Puzzle
On Thu, 22 Jul 2010 15:36:20 +1000, Grant wrote:
On Wed, 21 Jul 2010 20:02:50 -0700, Jim Thompson wrote: On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr wrote: John Larkin wrote: On Sat, 17 Jul 2010 02:42:20 -0400, ehsjr wrote: Paul Hovnanian P.E. wrote: My solution for the missing energy. But John's puzzle stated that energy *is* conserved, so there is no missing energy in his puzzle. He said _charge_ was not conserved, in some cases. Or maybe it's a different puzzle? What I recall was a 4F cap that was charged to .5 volts, therefore Q=2 coulombs. He magically cut in half. (I don't know why he didn't start with 2 caps, 2F each, in parallel.) The resultant 2F caps each retained the .5V charge for Q=1 coulomb per cap. He then puts them in series resulting in *a 1F cap charged to 1 volt* which is Q=1 coulomb, and claims there's 1 coulomb missing. That's the fallacy. The result is NOT a 1F cap. The result is 2 2F caps, in series. Each cap has Q=1 coulomb - there is no missing coulomb. Doesn't matter that total circuit C = 1 F. Ed But every 1F cap is, internally, two 2F caps in series. Just draw a dotted line midway through the dielectric. Play that game all you want. That "game" leads nowhere. It implies that all capacitors are internally a series string of infinitely small (physical) capacitors and infinitely large capacitance for each. This all reminds me of the 3 men rent a hotel room puzzle. The clerk tells them it will be 30 dollars, so each hands him a 10 dollar bill. Later, the clerk realizes he's made an error, the rate is only $25. So he gives 5 ones to the bellhop & instructs him to give the money back to the men. The bellhop can't divide it equally, so he goes to their room and hands each man a dollar, and pockets the other 2 bucks. Now, each man has gotten a dollar back, so each has given a total of $9 to the clerk. That's $27, and the bellhop has 2 bucks in his pocket. Where is the other dollar? After the two 1F caps are separated and rearranged in series, if you discharge them through a resistor, you will recover 1 coulomb. My point all along is that, in actual circuit design, the generalism "charge is conserved" is dangerous, given that "charge" is ampere-seconds that you can actually measure and use. Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. Ed John John "The Bloviator" Larkin obfuscates the obvious. There is no inconsistency. There is no magic. TINSTAAFL! TANSTAAFL! 'Aint', not 'isn't' ) I've read Larry Niven too. Grant. ...Jim Thompson I was just being politically correct ;-) ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | Spice is like a sports car... Only as good as the person behind the wheel. |
#5
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Two Cap Puzzle
On Thu, 22 Jul 2010 01:40:54 -0500, flipper wrote:
On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr wrote: [snip] Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. That only applies if your method of getting and putting is lossless but the general case in electronics is 100%. Ed "stuff" is the source of the error. ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | Spice is like a sports car... Only as good as the person behind the wheel. |
#6
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
Jim Thompson wrote:
On Thu, 22 Jul 2010 01:40:54 -0500, flipper wrote: On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr wrote: [snip] Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. That only applies if your method of getting and putting is lossless but the general case in electronics is 100%. Ed "stuff" is the source of the error. ...Jim Thompson Exactly. A coulomb is massless. It is not a fixed physical thing that occupies some particular volume, which seems to be the misconception at the heart of the so called puzzle. Ed |
#7
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Two Cap Puzzle
On Thu, 22 Jul 2010 13:43:51 -0400, ehsjr
wrote: Jim Thompson wrote: On Thu, 22 Jul 2010 01:40:54 -0500, flipper wrote: On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr wrote: [snip] Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. That only applies if your method of getting and putting is lossless but the general case in electronics is 100%. Ed "stuff" is the source of the error. ...Jim Thompson Exactly. A coulomb is massless. It is not a fixed physical thing that occupies some particular volume, which seems to be the misconception at the heart of the so called puzzle. Ed I'm not puzzled, John "The Bloviator" Larkin is. He asserts... [begin quoted message] NNTP-Posting-Date: Wed, 07 Jul 2010 10:50:55 -0500 From: John Larkin Newsgroups: sci.electronics.design Subject: Inverse Marx generator Date: Wed, 07 Jul 2010 08:50:50 -0700 Message-ID: [snip] Right. If you dump all the energy from one charged cap into another, discharged, cap of a different value, and do it efficiently, charge is not conserved. John [end quoted message] ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | Spice is like a sports car... Only as good as the person behind the wheel. |
#8
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
On Thu, 22 Jul 2010 15:04:36 -0500, flipper wrote:
On Thu, 22 Jul 2010 08:07:34 -0700, Jim Thompson wrote: On Thu, 22 Jul 2010 01:40:54 -0500, flipper wrote: On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr wrote: [snip] Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. That only applies if your method of getting and putting is lossless but the general case in electronics is 100%. Ed "stuff" is the source of the error. Which 'error' about which 'stuff' are we supposedly talking about here? Is it the series coulomb math error? ...Jim Thompson I'm trying to write it up, both I keep getting interrupted by work that pays $:-) ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | Spice is like a sports car... Only as good as the person behind the wheel. |
#9
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
flipper wrote:
On Thu, 22 Jul 2010 13:43:51 -0400, ehsjr wrote: Jim Thompson wrote: On Thu, 22 Jul 2010 01:40:54 -0500, flipper wrote: On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr wrote: [snip] Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. That only applies if your method of getting and putting is lossless but the general case in electronics is 100%. Ed "stuff" is the source of the error. ...Jim Thompson Exactly. A coulomb is massless. It is not a fixed physical thing An electrostatic field is massless. Are you trying to suggest an electrostatic field is not 'real'? that occupies some particular volume, In reality it does. Nope. I guess I didn't make my point clear. You can charge 2 different size (physical volume) caps with a coulomb. There is no particular volume associated with "a coulomb". which seems to be the misconception at the heart of the so called puzzle. If you are referring to the, so called, 'missing coulomb' there isn't one. Correct, there is no missing coulomb. I've already said that, earlier in the discussion. Ed snip |
#10
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Two Cap Puzzle
On Thu, 22 Jul 2010 13:43:51 -0400, ehsjr
wrote: Jim Thompson wrote: On Thu, 22 Jul 2010 01:40:54 -0500, flipper wrote: On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr wrote: [snip] Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. That only applies if your method of getting and putting is lossless but the general case in electronics is 100%. Ed "stuff" is the source of the error. ...Jim Thompson Exactly. A coulomb is massless. It is not a fixed physical thing that occupies some particular volume, which seems to be the misconception at the heart of the so called puzzle. Ed Good. Electron mobility in copper wire is the tinyest fraction of the speed of light. |
#11
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Two Cap Puzzle
"Jim Thompson" wrote in
message ... I'm trying to write it up, both I keep getting interrupted by work that pays $:-) ...Jim Thompson I'd be interested to see your write up, Jim. This conundrum was asked of me in a pre-uni interview more than 40 years ago, I forget my real answer, I think I doubted the assumption of zero resistance. There were some wacky claims by (I think it was) Ivor Catt in a discussion on this in Wireless World where he claimed it proved the existence of some wonderful new thingy ("displacement current"?). Much sound and fury, but little edification ensued as I recall. I should see if I still have the letters. It did cause me to be wary of "stated conditions" aka basic assumptions in engineering problems in later life ;-) Regards Ian |
#12
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Two Cap Puzzle
flipper wrote:
On Fri, 23 Jul 2010 00:12:50 -0400, ehsjr wrote: flipper wrote: On Thu, 22 Jul 2010 13:43:51 -0400, ehsjr wrote: Jim Thompson wrote: On Thu, 22 Jul 2010 01:40:54 -0500, flipper wrote: On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr wrote: [snip] Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. That only applies if your method of getting and putting is lossless but the general case in electronics is 100%. Ed "stuff" is the source of the error. ...Jim Thompson Exactly. A coulomb is massless. It is not a fixed physical thing An electrostatic field is massless. Are you trying to suggest an electrostatic field is not 'real'? that occupies some particular volume, In reality it does. Nope. I guess I didn't make my point clear. You can charge 2 different size (physical volume) caps with a coulomb. There is no particular volume associated with "a coulomb". I don't understand what you are trying to get at. Are you of the opinion that there is one particular volume, and one particular volume only, that a 1 coulomb charge will occupy? If so, what is that volume? If not, then you and I have no disagreement on the point. To go further. A coulomb is a numerical result of a mathematical operation, not a physical object. There is no physical object that is an "ampere second". A coulomb is massless, and volumeless. The puzzle misdirection appeared to be treating the coulomb as an object that could be divided by dividing that coulomb's container. Area and spacing, which define a volume, the dielectric of the volume and the applied volts determine the coulombs. It's not an 'arbitrary' thing and, in that sense, yes it is 'fixed' (by the particulars). Otherwise one would not be able to write an equation for it. It's even more the case when simply alternating between parallel or series connections as none of their parameters change, not even V (hence Q), and that's about as 'fixed' as one can get. which seems to be the misconception at the heart of the so called puzzle. If you are referring to the, so called, 'missing coulomb' there isn't one. Correct, there is no missing coulomb. I've already said that, earlier in the discussion. Ok. So I threaded back and, unless I misunderstood, you seem to be suggesting there is some unexplained 'difference' between whatever you deem a 'real' 1F capacitor and two 2s in series, despite their identical behavior, so that two 2s in series are "not a 1F cap" and 1F "doesn't matter." Not what I was suggesting. In the puzzle the 2 coulombs is a number that tells you how much current got stuffed into a container and how long the "stuffing" took. Magically dividing the container into two containers (or N containers) does not change the amount of current got stuffed in, nor the amount of time it took to do that stuffing. There's no need for mysterious 'differences' as, assuming all else is equal, a single 1F, two 2s in series, four 4s in series, eight 8s in series, and so on (although equal values are not required, just that the resulting series comes to 1F), are black box indistinguishable. At 1V overall they'll each and every one have 1 coulomb because they all have the exact same charging current go through. The puzzle's magic division creates the "mysterious differences" (it results in Vcap = V/N for each cap), hiding the fact that total ampere seconds is the same. You may have missed the context of the whole starting from the beginning, when a "puzzle" (which wasn't a puzzle at all) was presented. And I don't think it matters - the puzzle was just "mental gymnastics" that caused confusion instead of making a point, in my opinion. Your paragraph above shows you understand the principle, so the puzzle is irrelevant. And the op clarified his meaning: "My point all along is that, in actual circuit design, the generalism "charge is conserved" is dangerous, given that "charge" is ampere-seconds that you can actually measure and use." His "puzzle" was misdirection to show that a coulomb was somehow lost. No coulomb was lost. Perhaps what I've posted isn't clear to you, but if you think that no coulomb was lost in the puzzle, and that a coulomb of charge does not require one and only one specific volume, then we're in agreement. Ed Ed snip |
#13
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Two Cap Puzzle
On Sat, 24 Jul 2010 20:18:53 -0500, flipper wrote:
On Sat, 24 Jul 2010 15:29:45 -0400, ehsjr wrote: flipper wrote: On Fri, 23 Jul 2010 00:12:50 -0400, ehsjr wrote: flipper wrote: On Thu, 22 Jul 2010 13:43:51 -0400, ehsjr wrote: Jim Thompson wrote: On Thu, 22 Jul 2010 01:40:54 -0500, flipper wrote: On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr wrote: [snip] Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. That only applies if your method of getting and putting is lossless but the general case in electronics is 100%. Ed "stuff" is the source of the error. ...Jim Thompson Exactly. A coulomb is massless. It is not a fixed physical thing An electrostatic field is massless. Are you trying to suggest an electrostatic field is not 'real'? that occupies some particular volume, In reality it does. Nope. I guess I didn't make my point clear. You can charge 2 different size (physical volume) caps with a coulomb. There is no particular volume associated with "a coulomb". I don't understand what you are trying to get at. Are you of the opinion that there is one particular volume, and one particular volume only, that a 1 coulomb charge will occupy? If so, what is that volume? If not, then you and I have no disagreement on the point. Simply repeating the same thing doesn't explain it any more than the first time did. Changing the area/spacing ratios would, indeed, change the capacitance but it's irrelevant as the physical parameters are subsumed into the given capacitances and further irrelevant as none of the parameters change anyway. To go further. A coulomb is a numerical result of a mathematical operation, not a physical object. There is no physical object that is an "ampere second". A coulomb is massless, and volumeless. The puzzle misdirection appeared to be treating the coulomb as an object that could be divided by dividing that coulomb's container. It can. As you yourself pointed out, the story might as well begin with two 2s in parallel and skip the fluff of 'splitting' the 4 in half as the result is the same and nothing mysterious happens. You have two 2F capacitors each with a 'charge' (Q) of 1 coulomb. And as I pointed out, the entire parallel step is entirely superfluous as you have the same supposed 'mystery' if you just look at two 2's in series. Each have 1 coulomb and the total has one coulomb. Of course, as I also explained, there is no 'mystery' because coulombs do not add in series. They each and all have the same Q as the whole because the exact same current goes through each and all as the whole. I.E. instead of the 'mystery' posited by the diversion 1 + 1 = 1, "huh where's the missing coulomb?" the correct answer is 1 = 1 = 1, just as it should. Area and spacing, which define a volume, the dielectric of the volume and the applied volts determine the coulombs. It's not an 'arbitrary' thing and, in that sense, yes it is 'fixed' (by the particulars). Otherwise one would not be able to write an equation for it. It's even more the case when simply alternating between parallel or series connections as none of their parameters change, not even V (hence Q), and that's about as 'fixed' as one can get. which seems to be the misconception at the heart of the so called puzzle. If you are referring to the, so called, 'missing coulomb' there isn't one. Correct, there is no missing coulomb. I've already said that, earlier in the discussion. Ok. So I threaded back and, unless I misunderstood, you seem to be suggesting there is some unexplained 'difference' between whatever you deem a 'real' 1F capacitor and two 2s in series, despite their identical behavior, so that two 2s in series are "not a 1F cap" and 1F "doesn't matter." Not what I was suggesting. Ok. Then what did the two 2s are "not a 1F cap" and 1F "doesn't matter" mean? In the puzzle the 2 coulombs is a number that tells you how much current got stuffed into a container and how long the "stuffing" took. Magically dividing the container into two containers (or N containers) does not change the amount of current got stuffed in, nor the amount of time it took to do that stuffing. Exactly. So what is the machination on "volume" about? There's no need for mysterious 'differences' as, assuming all else is equal, a single 1F, two 2s in series, four 4s in series, eight 8s in series, and so on (although equal values are not required, just that the resulting series comes to 1F), are black box indistinguishable. At 1V overall they'll each and every one have 1 coulomb because they all have the exact same charging current go through. The puzzle's magic division creates the "mysterious differences" (it results in Vcap = V/N for each cap), Not so. Capacitors in parallel have the same V and still do when then 'disconnected' from each other (since they're 'ideal' with no leakage).. hiding the fact that total ampere seconds is the same. There's nothing 'hidden' about 2 parallel coulombs divided into two being 1 coulomb each. Albeit superfluous the parallel step is entirely accurate. You begin with .5V on 4F for 2 coulombs and you end up with two 2s each with .5V and 1 coulomb. 'Volume', dielectric, and all other physical parameters are irrelevant as they are subsumed into the 'given' capacitances. It doesn't matter how they are made as 2F is 2F. In parallel it's 4F and in series it's 1F. That's it. You may have missed the context of the whole starting from the beginning, when a "puzzle" (which wasn't a puzzle at all) was presented. Paul Hovnanian started the thread with a proposed 'solution' to the 'cap charging a cap' puzzle and mine was the first reply. All I did was point out that the 'solution' was equivalent to the oft posited voltage source charging an 'ideal' cap 'puzzle' and that substituting a cap for the voltage source simply makes the puzzle appear more mysterious than it is. (A sub thread then ensued about R=0) You introduced the 'parallel to series' puzzle and I think I am the only one in this thread, so far, to explain it. And I don't think it matters - the puzzle was just "mental gymnastics" that caused confusion instead of making a point, in my opinion. The purpose of a 'puzzle' is to posit what appears to be a conundrum for the reader to then figure out. The 'mystery' of the original puzzle is in leaving series R out of the model and the 'mystery' of the second is being diverted into thinking coulombs should 'add' when, in series, they do not. Your paragraph above shows you understand the principle, so the puzzle is irrelevant. And the op clarified his meaning: "My point all along is that, in actual circuit design, the generalism "charge is conserved" is dangerous, given that "charge" is ampere-seconds that you can actually measure and use." His "puzzle" was misdirection to show that a coulomb was somehow lost. No coulomb was lost. That was John Larkin and he was neither the OP nor did he posit either of the 'puzzles'. His first entry was to me and I did not respond because he hacked my words to imply I said things I did not and changed the model to boot so it wasn't even relevant to the discussion. Perhaps what I've posted isn't clear to you, but if you think that no coulomb was lost in the puzzle, and that a coulomb of charge does not require one and only one specific volume, then we're in agreement. You still seem to be positing some 'mysterious' thing about 'volume' that has nothing to do with solving the puzzle. Maybe if you put it to numbers I could gather what you mean. Here's my math Q(Coulombs) = CV, E(Joules) = .5QV (or, by substitution, .5CV^2) Each: 2F, .5V, 1C, .25J Parallel: 2F + 2F = 4F, .5V = .5V = .5V, 1C + 1C = 2C, .5J Series: 1/(1/2F + 1/2F) = 1F, .5V + .5V = 1V, 1C = 1C = 1C, .5J Note that 'Q per volume' (whatever it might be) of the 2F caps remains 'fixed' because neither Q nor 'volume' change and neither does V, or anything else. Or at least we can chose to 'pick' that simpler case because 'volume' is not mentioned anywhere since, being subsumed into F, it's completely irrelevant. Energy is conserved, 'charge' (Q) is conserved, and all is right with the world. There is no 'puzzle' unless one is fooled by the riddle into thinking series coulombs should add. Ed Ed snip Unless your business is located in San Fransicko, Californica ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | Spice is like a sports car... Only as good as the person behind the wheel. |
#14
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
flipper wrote:
On Sat, 24 Jul 2010 15:29:45 -0400, ehsjr wrote: flipper wrote: On Fri, 23 Jul 2010 00:12:50 -0400, ehsjr wrote: flipper wrote: On Thu, 22 Jul 2010 13:43:51 -0400, ehsjr wrote: Jim Thompson wrote: On Thu, 22 Jul 2010 01:40:54 -0500, flipper wrote: On Wed, 21 Jul 2010 22:45:33 -0400, ehsjr wrote: [snip] Well, I don't see any inconsistancy in putting "stuff" in at one rate, and getting that "stuff" out at another, whether it's water into bottles, cookies into bags, electrons into conductors, whatever. You get the same amount of "stuff" out as you put in (assuming you empty the container), but the time taken to do it is different. That only applies if your method of getting and putting is lossless but the general case in electronics is 100%. Ed "stuff" is the source of the error. ...Jim Thompson Exactly. A coulomb is massless. It is not a fixed physical thing An electrostatic field is massless. Are you trying to suggest an electrostatic field is not 'real'? that occupies some particular volume, In reality it does. Nope. I guess I didn't make my point clear. You can charge 2 different size (physical volume) caps with a coulomb. There is no particular volume associated with "a coulomb". I don't understand what you are trying to get at. Are you of the opinion that there is one particular volume, and one particular volume only, that a 1 coulomb charge will occupy? If so, what is that volume? If not, then you and I have no disagreement on the point. Simply repeating the same thing doesn't explain it any more than the first time did. You did not answer the question. Apparently you can't/won't or just want to argue. I'll try, one last time: You don't seem to realize that a coulomb is not a physical object. It is a number, the result of a mathematical operation on amperes and seconds. Thus all "puzzles" that attempt to treat it as a physical object with mass and volume are flawed at the outset. I have been trying to point out that it seems that the puzzle that JL posed uses the misdirection of trying to get the reader to think that the "stuff" in the cap called a coulomb is an object, a thing with mass and volume. Maybe that is not the intended misdirection, but you and I can't get past the point of agreeing on what volume means. A coulomb does not have the property of volume or mass. Whatever object has been charged does but the coulomb itself is just a number. I'm sorry if that is a repeat, but it is a fact you don't agree to. We can't get any further. I do need to correct 2 points you made below: "You introduced the 'parallel to series' puzzle and I think I am the only one in this thread, so far, to explain it." Do not lay that puzzle at my doorstep! :-) (Well, unless you want to stomp on it. Even then attribute "ownership" where it belongs. :-) ) John introduced the parallel to series puzzle elsewhere. I attributed it to him in my post. And it's clear from the context that I'm talking about what someone else posted. "That was John Larkin and he was neither the OP nor did he posit either of the 'puzzles'." He posted the 'parallel to series' puzzle on SED - obviously you missed it. In any event, it is not *my* puzzle, and I didn't pose it. Ed Changing the area/spacing ratios would, indeed, change the capacitance but it's irrelevant as the physical parameters are subsumed into the given capacitances and further irrelevant as none of the parameters change anyway. To go further. A coulomb is a numerical result of a mathematical operation, not a physical object. There is no physical object that is an "ampere second". A coulomb is massless, and volumeless. The puzzle misdirection appeared to be treating the coulomb as an object that could be divided by dividing that coulomb's container. It can. As you yourself pointed out, the story might as well begin with two 2s in parallel and skip the fluff of 'splitting' the 4 in half as the result is the same and nothing mysterious happens. You have two 2F capacitors each with a 'charge' (Q) of 1 coulomb. And as I pointed out, the entire parallel step is entirely superfluous as you have the same supposed 'mystery' if you just look at two 2's in series. Each have 1 coulomb and the total has one coulomb. Of course, as I also explained, there is no 'mystery' because coulombs do not add in series. They each and all have the same Q as the whole because the exact same current goes through each and all as the whole. I.E. instead of the 'mystery' posited by the diversion 1 + 1 = 1, "huh where's the missing coulomb?" the correct answer is 1 = 1 = 1, just as it should. Area and spacing, which define a volume, the dielectric of the volume and the applied volts determine the coulombs. It's not an 'arbitrary' thing and, in that sense, yes it is 'fixed' (by the particulars). Otherwise one would not be able to write an equation for it. It's even more the case when simply alternating between parallel or series connections as none of their parameters change, not even V (hence Q), and that's about as 'fixed' as one can get. which seems to be the misconception at the heart of the so called puzzle. If you are referring to the, so called, 'missing coulomb' there isn't one. Correct, there is no missing coulomb. I've already said that, earlier in the discussion. Ok. So I threaded back and, unless I misunderstood, you seem to be suggesting there is some unexplained 'difference' between whatever you deem a 'real' 1F capacitor and two 2s in series, despite their identical behavior, so that two 2s in series are "not a 1F cap" and 1F "doesn't matter." Not what I was suggesting. Ok. Then what did the two 2s are "not a 1F cap" and 1F "doesn't matter" mean? In the puzzle the 2 coulombs is a number that tells you how much current got stuffed into a container and how long the "stuffing" took. Magically dividing the container into two containers (or N containers) does not change the amount of current got stuffed in, nor the amount of time it took to do that stuffing. Exactly. So what is the machination on "volume" about? There's no need for mysterious 'differences' as, assuming all else is equal, a single 1F, two 2s in series, four 4s in series, eight 8s in series, and so on (although equal values are not required, just that the resulting series comes to 1F), are black box indistinguishable. At 1V overall they'll each and every one have 1 coulomb because they all have the exact same charging current go through. The puzzle's magic division creates the "mysterious differences" (it results in Vcap = V/N for each cap), Not so. Capacitors in parallel have the same V and still do when then 'disconnected' from each other (since they're 'ideal' with no leakage).. hiding the fact that total ampere seconds is the same. There's nothing 'hidden' about 2 parallel coulombs divided into two being 1 coulomb each. Albeit superfluous the parallel step is entirely accurate. You begin with .5V on 4F for 2 coulombs and you end up with two 2s each with .5V and 1 coulomb. 'Volume', dielectric, and all other physical parameters are irrelevant as they are subsumed into the 'given' capacitances. It doesn't matter how they are made as 2F is 2F. In parallel it's 4F and in series it's 1F. That's it. You may have missed the context of the whole starting from the beginning, when a "puzzle" (which wasn't a puzzle at all) was presented. Paul Hovnanian started the thread with a proposed 'solution' to the 'cap charging a cap' puzzle and mine was the first reply. All I did was point out that the 'solution' was equivalent to the oft posited voltage source charging an 'ideal' cap 'puzzle' and that substituting a cap for the voltage source simply makes the puzzle appear more mysterious than it is. (A sub thread then ensued about R=0) You introduced the 'parallel to series' puzzle and I think I am the only one in this thread, so far, to explain it. And I don't think it matters - the puzzle was just "mental gymnastics" that caused confusion instead of making a point, in my opinion. The purpose of a 'puzzle' is to posit what appears to be a conundrum for the reader to then figure out. The 'mystery' of the original puzzle is in leaving series R out of the model and the 'mystery' of the second is being diverted into thinking coulombs should 'add' when, in series, they do not. Your paragraph above shows you understand the principle, so the puzzle is irrelevant. And the op clarified his meaning: "My point all along is that, in actual circuit design, the generalism "charge is conserved" is dangerous, given that "charge" is ampere-seconds that you can actually measure and use." His "puzzle" was misdirection to show that a coulomb was somehow lost. No coulomb was lost. That was John Larkin and he was neither the OP nor did he posit either of the 'puzzles'. His first entry was to me and I did not respond because he hacked my words to imply I said things I did not and changed the model to boot so it wasn't even relevant to the discussion. Perhaps what I've posted isn't clear to you, but if you think that no coulomb was lost in the puzzle, and that a coulomb of charge does not require one and only one specific volume, then we're in agreement. You still seem to be positing some 'mysterious' thing about 'volume' that has nothing to do with solving the puzzle. Maybe if you put it to numbers I could gather what you mean. Here's my math Q(Coulombs) = CV, E(Joules) = .5QV (or, by substitution, .5CV^2) Each: 2F, .5V, 1C, .25J Parallel: 2F + 2F = 4F, .5V = .5V = .5V, 1C + 1C = 2C, .5J Series: 1/(1/2F + 1/2F) = 1F, .5V + .5V = 1V, 1C = 1C = 1C, .5J Note that 'Q per volume' (whatever it might be) of the 2F caps remains 'fixed' because neither Q nor 'volume' change and neither does V, or anything else. Or at least we can chose to 'pick' that simpler case because 'volume' is not mentioned anywhere since, being subsumed into F, it's completely irrelevant. Energy is conserved, 'charge' (Q) is conserved, and all is right with the world. There is no 'puzzle' unless one is fooled by the riddle into thinking series coulombs should add. Ed Ed snip |
#15
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
On Sun, 25 Jul 2010 23:09:57 -0500, flipper wrote:
On Sat, 24 Jul 2010 17:31:57 +0100, "Ian" wrote: "Jim Thompson" wrote in message ... I'm trying to write it up, both I keep getting interrupted by work that pays $:-) ...Jim Thompson I'd be interested to see your write up, Jim. This conundrum was asked of me in a pre-uni interview more than 40 years ago, I forget my real answer, I think I doubted the assumption of zero resistance. There were some wacky claims by (I think it was) Ivor Catt in a discussion on this in Wireless World where he claimed it proved the existence of some wonderful new thingy ("displacement current"?). Much sound and fury, but little edification ensued as I recall. I should see if I still have the letters. My understanding is that Ivor Catt doesn't believe in displacement current or much else of conventional electromagnetism. http://en.wikipedia.org/wiki/Ivor_Catt http://en.wikipedia.org/wiki/Displacement_current It did cause me to be wary of "stated conditions" aka basic assumptions in engineering problems in later life ;-) A wise caution. Regards Ian "Ivor Catt" sounds like I should know him... '50's, early '60's ??? ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | Spice is like a sports car... Only as good as the person behind the wheel. |
#16
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
On Mon, 26 Jul 2010 00:33:58 -0500, flipper wrote:
On Sun, 25 Jul 2010 21:31:45 -0700, Jim Thompson wrote: On Sun, 25 Jul 2010 23:09:57 -0500, flipper wrote: On Sat, 24 Jul 2010 17:31:57 +0100, "Ian" wrote: "Jim Thompson" wrote in message ... I'm trying to write it up, both I keep getting interrupted by work that pays $:-) ...Jim Thompson I'd be interested to see your write up, Jim. This conundrum was asked of me in a pre-uni interview more than 40 years ago, I forget my real answer, I think I doubted the assumption of zero resistance. There were some wacky claims by (I think it was) Ivor Catt in a discussion on this in Wireless World where he claimed it proved the existence of some wonderful new thingy ("displacement current"?). Much sound and fury, but little edification ensued as I recall. I should see if I still have the letters. My understanding is that Ivor Catt doesn't believe in displacement current or much else of conventional electromagnetism. http://en.wikipedia.org/wiki/Ivor_Catt http://en.wikipedia.org/wiki/Displacement_current It did cause me to be wary of "stated conditions" aka basic assumptions in engineering problems in later life ;-) A wise caution. Regards Ian "Ivor Catt" sounds like I should know him... '50's, early '60's ??? Well, the wikipedia article says he was born in 1935 so that would make him around 75. ...Jim Thompson I was talking of the year-range where I think I met him... possibly at Motorola. With a name like that, one rarely forgets :-) ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | Spice is like a sports car... Only as good as the person behind the wheel. |
#17
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
flipper wrote:
much snipped Where you claim the 'puzzle' lies, 'splitting' the 4F into two 2s, there's no puzzle at all. That is not what I said at all. I have no problem with magically cutting the 4F charged to .5 volts and Q=2cap into 2 2F caps each charged to .5 volts with Q=1 for each cap, as the puzzle proposes. As I explained, you have the ENTIRE 'puzzle' if you just put two 2s in series and charge them up to 1V. Ok, _now_ I see what you are missing. That is most definitely NOT in the puzzle. The caps were not *charged* in series. You missed what the puzzle says. Both 2F capacitors have 1 coulomb and the whole 1F capacitor has one coulomb. 1 + 1 = 1. Where is the missing coulomb? I don't understand your point above - I'm guessing that you're indicating that coulombs don't add. But you are referring to the wrong scenario, in any event. Not ONE thing 'changes'. They are completely static with not even a connection change. Explain that one with your 'volumes'. Don't be absurd. The puzzle stipulates changes. The only misdirection is in thinking coulombs add in series when they don't. Here http://farside.ph.utexas.edu/teachin...es/node46.html Two capacitors connected in series. "... the fact that the charge is common to all three capacitors. " Your cite above refers to a non-isolated system. You jumped into the middle of an ongoing metadiscussion that started on SED, so you are not aware of what has gone before. There was a large amount of discussion on conservation of charge, and it spanned more than one subject. JL made the point that charge is sometimes not conserved. I'll cut and paste the puzzle as he wrote it, below my comments. His puzzle takes an isolated system, that starts out *already* charged with 2 coulombs, and monkeys around with the volumes inside the system. Your cite above refers to a non isolated system, and is not applicable to an isolated system. If you don't like the use of the word volume, fine. Substitute whatever term you want that includes the concept of the capacity of that volume and the coordinates that describe the place where your chosen term exists. Or use whatever term(s) that allow you to realize that 2 2F capacitors in series are NOT *a* 1F capacitor in the puzzle, without getting sidetracked into thinking that 1/Ct = 1/C1+1/C2...1/Cn applies to the isolated system. The law of conservation of charge applies as long as the system remains isolated. The number of coulombs remains constant, regardless of the volume (size, whatever your term is) of the pieces you magically slice the original cap into, or how you connect them, in that isolated system. The puzzle ends up stating that after the slicing & serial connecting, you have *a* 1F cap charged to 1 volt. That is *false*. You have 2 2F caps, each with a charge of 1 coulomb, connected in series. Now, because Q = CV, and because charge is constant in an isolated system and you started with 2 coulombs charge, if you magically merged the two caps into a 1F cap, then Q=CV means that V would have to be 2, not 1. Charge must be conserved. As I used "volume", those two caps occupy different cordinates, they are not the magical merger the puzzle implies into a 1F cap, and they must be considered as such: 2 separate capacitors, not a single 1F capacitor. Different volumes, no merger of coordinates, no merger of capacity. There's no current in or out of either cap. It simply does not matter, in the isolated system, that the total series capacitance would equal 1F in a non isolated system. The misdirection seems to me to be in the monkeying around with the volumes. It states that you have a 1F cap. In fact you don't even have the equivalent of a 1F cap. The fact that you have 2 2F caps with an equivalent of a single 1F *if connected in series in a circuit* becomes important when you make the system no longer isolated by discharging. But the puzzle does *not* "un-isolate" the system. No current flows. The serial caps are just two caps, each of which has one of its leads connected to the other cap, and its other lead floating free. There is no circuit. Those two caps might just as well be lying in your parts drawer. There is no equivalent capacitance. Ed I can't begin to capture the whole metadiscussion, which spans several subjects and 2 (or more?) newsgroups, but at least I can quote the part where John posted the puzzle: Quoting from John Larkin's post, 7/10/2010 at 11:16 AM on SED. Subject: Win Hill: Inverse Marx Generator ?? To celebrate the 21st century, I have composed a new riddle: Start with a 4 farad cap charged to 0.5 volts. Q = 2 coulombs. Carefully saw it in half, without discharging it, such as to have two caps, each 2 farads, each charged to 0.5 volts. The total charge of the two caps remains 2 coulombs, whether you connect them in parallel or consider them separately. Now stack them in series. The result is a 1F cap charged to 1 volt. That has a charge of 1 coulomb. Where did the other coulomb go? I think this is a better riddle. John Maybe that is not the intended misdirection, but you and I can't get past the point of agreeing on what volume means. Really. Where did I ever dispute the meaning of 'volume'? A coulomb does not have the property of volume or mass. And volume or mass does not have the property of charge, spin, or color. So what? You act as if the only 'real' things in the universe are volume and mass so that all else are "only numbers;" and mysterious magical ones that invisibly 'change' when nothing else has. Whatever object has been charged does but the coulomb itself is just a number. And volume is "just a number." Volume is the product of measurable quantities. Coulombs is the product of measurable quantities. We can measure volume. We can measure coulombs. There is no mysticism involved. I'm sorry if that is a repeat, but it is a fact you don't agree to. We can't get any further. You can't go any further because you can't put any math to your 'volume' theory, which means you have not solved the 'puzzle' as arm waving about unexplained 'volume effects' does not solve equations. I do need to correct 2 points you made below: "You introduced the 'parallel to series' puzzle and I think I am the only one in this thread, so far, to explain it." Do not lay that puzzle at my doorstep! :-) (Well, unless you want to stomp on it. Even then attribute "ownership" where it belongs. :-) ) I didn't say you invented or 'owned' it. I said you introduced it here. John introduced the parallel to series puzzle elsewhere. If you say so. I attributed it to him in my post. And it's clear from the context that I'm talking about what someone else posted. Terrific. And thank you for introducing it to us. "That was John Larkin and he was neither the OP nor did he posit either of the 'puzzles'." He posted the 'parallel to series' puzzle on SED - obviously you missed it. This isn't SED, it's ABSE. In any event, it is not *my* puzzle, and I didn't pose it. I didn't say either. All I said is you introduced it. Good Lord, you act as if mentioning it is a heinous crime you plead not guilty to. Ed Changing the area/spacing ratios would, indeed, change the capacitance but it's irrelevant as the physical parameters are subsumed into the given capacitances and further irrelevant as none of the parameters change anyway. To go further. A coulomb is a numerical result of a mathematical operation, not a physical object. There is no physical object that is an "ampere second". A coulomb is massless, and volumeless. The puzzle misdirection appeared to be treating the coulomb as an object that could be divided by dividing that coulomb's container. It can. As you yourself pointed out, the story might as well begin with two 2s in parallel and skip the fluff of 'splitting' the 4 in half as the result is the same and nothing mysterious happens. You have two 2F capacitors each with a 'charge' (Q) of 1 coulomb. And as I pointed out, the entire parallel step is entirely superfluous as you have the same supposed 'mystery' if you just look at two 2's in series. Each have 1 coulomb and the total has one coulomb. Of course, as I also explained, there is no 'mystery' because coulombs do not add in series. They each and all have the same Q as the whole because the exact same current goes through each and all as the whole. I.E. instead of the 'mystery' posited by the diversion 1 + 1 = 1, "huh where's the missing coulomb?" the correct answer is 1 = 1 = 1, just as it should. Area and spacing, which define a volume, the dielectric of the volume and the applied volts determine the coulombs. It's not an 'arbitrary' thing and, in that sense, yes it is 'fixed' (by the particulars). Otherwise one would not be able to write an equation for it. It's even more the case when simply alternating between parallel or series connections as none of their parameters change, not even V (hence Q), and that's about as 'fixed' as one can get. which seems to be the misconception at the heart of the so called puzzle. If you are referring to the, so called, 'missing coulomb' there isn't one. Correct, there is no missing coulomb. I've already said that, earlier in the discussion. Ok. So I threaded back and, unless I misunderstood, you seem to be suggesting there is some unexplained 'difference' between whatever you deem a 'real' 1F capacitor and two 2s in series, despite their identical behavior, so that two 2s in series are "not a 1F cap" and 1F "doesn't matter." Not what I was suggesting. Ok. Then what did the two 2s are "not a 1F cap" and 1F "doesn't matter" mean? In the puzzle the 2 coulombs is a number that tells you how much current got stuffed into a container and how long the "stuffing" took. Magically dividing the container into two containers (or N containers) does not change the amount of current got stuffed in, nor the amount of time it took to do that stuffing. Exactly. So what is the machination on "volume" about? There's no need for mysterious 'differences' as, assuming all else is equal, a single 1F, two 2s in series, four 4s in series, eight 8s in series, and so on (although equal values are not required, just that the resulting series comes to 1F), are black box indistinguishable. At 1V overall they'll each and every one have 1 coulomb because they all have the exact same charging current go through. The puzzle's magic division creates the "mysterious differences" (it results in Vcap = V/N for each cap), Not so. Capacitors in parallel have the same V and still do when then 'disconnected' from each other (since they're 'ideal' with no leakage).. hiding the fact that total ampere seconds is the same. There's nothing 'hidden' about 2 parallel coulombs divided into two being 1 coulomb each. Albeit superfluous the parallel step is entirely accurate. You begin with .5V on 4F for 2 coulombs and you end up with two 2s each with .5V and 1 coulomb. 'Volume', dielectric, and all other physical parameters are irrelevant as they are subsumed into the 'given' capacitances. It doesn't matter how they are made as 2F is 2F. In parallel it's 4F and in series it's 1F. That's it. You may have missed the context of the whole starting from the beginning, when a "puzzle" (which wasn't a puzzle at all) was presented. Paul Hovnanian started the thread with a proposed 'solution' to the 'cap charging a cap' puzzle and mine was the first reply. All I did was point out that the 'solution' was equivalent to the oft posited voltage source charging an 'ideal' cap 'puzzle' and that substituting a cap for the voltage source simply makes the puzzle appear more mysterious than it is. (A sub thread then ensued about R=0) You introduced the 'parallel to series' puzzle and I think I am the only one in this thread, so far, to explain it. And I don't think it matters - the puzzle was just "mental gymnastics" that caused confusion instead of making a point, in my opinion. The purpose of a 'puzzle' is to posit what appears to be a conundrum for the reader to then figure out. The 'mystery' of the original puzzle is in leaving series R out of the model and the 'mystery' of the second is being diverted into thinking coulombs should 'add' when, in series, they do not. Your paragraph above shows you understand the principle, so the puzzle is irrelevant. And the op clarified his meaning: "My point all along is that, in actual circuit design, the generalism "charge is conserved" is dangerous, given that "charge" is ampere-seconds that you can actually measure and use." His "puzzle" was misdirection to show that a coulomb was somehow lost. No coulomb was lost. That was John Larkin and he was neither the OP nor did he posit either of the 'puzzles'. His first entry was to me and I did not respond because he hacked my words to imply I said things I did not and changed the model to boot so it wasn't even relevant to the discussion. Perhaps what I've posted isn't clear to you, but if you think that no coulomb was lost in the puzzle, and that a coulomb of charge does not require one and only one specific volume, then we're in agreement. You still seem to be positing some 'mysterious' thing about 'volume' that has nothing to do with solving the puzzle. Maybe if you put it to numbers I could gather what you mean. Here's my math Q(Coulombs) = CV, E(Joules) = .5QV (or, by substitution, .5CV^2) Each: 2F, .5V, 1C, .25J Parallel: 2F + 2F = 4F, .5V = .5V = .5V, 1C + 1C = 2C, .5J Series: 1/(1/2F + 1/2F) = 1F, .5V + .5V = 1V, 1C = 1C = 1C, .5J Note that 'Q per volume' (whatever it might be) of the 2F caps remains 'fixed' because neither Q nor 'volume' change and neither does V, or anything else. Or at least we can chose to 'pick' that simpler case because 'volume' is not mentioned anywhere since, being subsumed into F, it's completely irrelevant. Energy is conserved, 'charge' (Q) is conserved, and all is right with the world. There is no 'puzzle' unless one is fooled by the riddle into thinking series coulombs should add. Ed Ed snip |
#18
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Two Cap Puzzle
On Mon, 26 Jul 2010 15:37:12 -0500, flipper wrote:
On Mon, 26 Jul 2010 07:57:11 -0700, Jim Thompson wrote: On Mon, 26 Jul 2010 00:33:58 -0500, flipper wrote: On Sun, 25 Jul 2010 21:31:45 -0700, Jim Thompson wrote: On Sun, 25 Jul 2010 23:09:57 -0500, flipper wrote: On Sat, 24 Jul 2010 17:31:57 +0100, "Ian" wrote: "Jim Thompson" wrote in message ... I'm trying to write it up, both I keep getting interrupted by work that pays $:-) ...Jim Thompson I'd be interested to see your write up, Jim. This conundrum was asked of me in a pre-uni interview more than 40 years ago, I forget my real answer, I think I doubted the assumption of zero resistance. There were some wacky claims by (I think it was) Ivor Catt in a discussion on this in Wireless World where he claimed it proved the existence of some wonderful new thingy ("displacement current"?). Much sound and fury, but little edification ensued as I recall. I should see if I still have the letters. My understanding is that Ivor Catt doesn't believe in displacement current or much else of conventional electromagnetism. http://en.wikipedia.org/wiki/Ivor_Catt http://en.wikipedia.org/wiki/Displacement_current It did cause me to be wary of "stated conditions" aka basic assumptions in engineering problems in later life ;-) A wise caution. Regards Ian "Ivor Catt" sounds like I should know him... '50's, early '60's ??? Well, the wikipedia article says he was born in 1935 so that would make him around 75. ...Jim Thompson I was talking of the year-range where I think I met him... possibly at Motorola. With a name like that, one rarely forgets :-) Oh. Well, how in the world would I know THAT? LOL I do see references to him at Motorola. One says 'mid' 1960s and the other said 'late' 1960s. I also see 1964 and 1966 referenced in some papers. ...Jim Thompson OK. I was Moto from 6/62 to 11/70 ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | Spice is like a sports car... Only as good as the person behind the wheel. |
#19
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Two Cap Puzzle
On Mon, 26 Jul 2010 18:03:11 -0400, ehsjr
wrote: [snip] I can't begin to capture the whole metadiscussion, which spans several subjects and 2 (or more?) newsgroups, but at least I can quote the part where John posted the puzzle: Quoting from John Larkin's post, 7/10/2010 at 11:16 AM on SED. Subject: Win Hill: Inverse Marx Generator ?? To celebrate the 21st century, I have composed a new riddle: Start with a 4 farad cap charged to 0.5 volts. Q = 2 coulombs. Carefully saw it in half, without discharging it, such as to have two caps, each 2 farads, each charged to 0.5 volts. The total charge of the two caps remains 2 coulombs, whether you connect them in parallel or consider them separately. Now stack them in series. The result is a 1F cap charged to 1 volt. That has a charge of 1 coulomb. Where did the other coulomb go? I think this is a better riddle. John [snip] No riddle at all for anyone who even doodles a single picture (after reading the Wiki Conservation of Charge Page) ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | SED Has Crumbled to Below SEB Status Populated Only by Bloviators and Pompous PhD's |
#20
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Two Cap Puzzle
On Mon, 26 Jul 2010 15:59:32 -0700, Jim Thompson wrote:
.... Populated Only by Bloviators and Pompous PhD's Here I was, thinking you made that word up, so google found for me: " According to WikiPedia, to bloviate is to "speak pompously and excessively", or "to expound ridiculously". A colloquial verb coined in the United States, it is commonly used with contempt to describe the behavior of politicians, academics, pundits or media "experts", sometimes called bloviators, who hold forth on subjects in an arrogant, tiresome way. " -- http://www.bloviators.net/ There, they have their very own website! Grant. |
#21
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Two Cap Puzzle
On Tue, 27 Jul 2010 00:21:20 -0500, flipper wrote:
On Mon, 26 Jul 2010 18:03:11 -0400, ehsjr wrote: flipper wrote: much snipped Where you claim the 'puzzle' lies, 'splitting' the 4F into two 2s, there's no puzzle at all. That is not what I said at all. I have no problem with magically cutting the 4F charged to .5 volts and Q=2cap into 2 2F caps each charged to .5 volts with Q=1 for each cap, as the puzzle proposes. Terrific. As I explained, you have the ENTIRE 'puzzle' if you just put two 2s in series and charge them up to 1V. Ok, _now_ I see what you are missing. That is most definitely NOT in the puzzle. The caps were not *charged* in series. You missed what the puzzle says. No, I did not 'miss' what the puzzle says. It's irrelevant as it makes NO difference if you 'charge' them in parallel, in series, or separately. The math is IDENTICAL, which is why I explained that the parallel step is superfluous and you might as well start with them in series. You have EXACTLY the same situation. Both 2F capacitors have 1 coulomb and the whole 1F capacitor has one coulomb. 1 + 1 = 1. Where is the missing coulomb? I don't understand your point above - I'm guessing that you're indicating that coulombs don't add. That's right. Coulombs do not add in series. But you are referring to the wrong scenario, in any event. No I am not. It is the exact same "scenario" as it does not matter 'how' 1 coulomb gets in the 2F cap. .5V on 2F is 1 coulomb is 1 coulomb is 1 coulomb. Put the two 2s in parallel, charge them to .5V, and you have 1 coulomb on each. Charge them in series to 1V overall and you have 1 coulomb on each. Charge them separately to .5V and you have 1 coulomb on each. It DOES NOT MATTER. 1 coulomb is 1 coulomb is 1 coulomb. Not ONE thing 'changes'. They are completely static with not even a connection change. Explain that one with your 'volumes'. Don't be absurd. The puzzle stipulates changes. Nope. The 2F caps have .5V for 1 coulomb throughout the entire exercise. NOTHING about the capacitors and their charge changes. The only misdirection is in thinking coulombs add in series when they don't. Here http://farside.ph.utexas.edu/teachin...es/node46.html Two capacitors connected in series. "... the fact that the charge is common to all three capacitors. " Your cite above refers to a non-isolated system. Oh? And just what are the bare wires sticking out each end 'connected' to? Doesn't matter anyway. Volts are Volts and Farads are Farads. You jumped into the middle of an ongoing metadiscussion that started on SED, so you are not aware of what has gone before. There was a large amount of discussion on conservation of charge, and it spanned more than one subject. JL made the point that charge is sometimes not conserved. Doesn't matter what went on before. Capacitors can't read nor do they care what sense or nonsense someone wrote. I'll cut and paste the puzzle as he wrote it, below my comments. His puzzle takes an isolated system, that starts out *already* charged with 2 coulombs, and monkeys around with the volumes inside the system. Your cite above refers to a non isolated system, and is not applicable to an isolated system. You see any reference to 'volumes' in CV? No. It's irrelevant. If you don't like the use of the word volume, fine. Substitute whatever term you want that includes the concept of the capacity of that volume and the coordinates that describe the place where your chosen term exists. Or use whatever term(s) that allow you to realize that 2 2F capacitors in series are NOT *a* 1F capacitor in the puzzle, without getting sidetracked into thinking that 1/Ct = 1/C1+1/C2...1/Cn applies to the isolated system. You, again, try to make hay from nonsense. Do you see anything in the equations that qualify 'how' a "1F capacitor" is 'made'? No. It doesn't matter if I use two plates or a hundred little plates in parallel or a dozen large plates in series or a combination. Farads are Farads. Two 2s in series ARE "a 1F capacitor" and 1/Ct = 1/C1+1/C2...1/Cn is not a 'sidetrack', it's a measurable fact. If it makes you feel any better then pot them in a tube with two leads sticking out. It's 1F. The law of conservation of charge applies as long as the system remains isolated. The number of coulombs remains constant, regardless of the volume (size, whatever your term is) of the pieces you magically slice the original cap into, or how you connect them, in that isolated system. The puzzle ends up stating that after the slicing & serial connecting, you have *a* 1F cap charged to 1 volt. That is *false*. It is perfectly true. You DO have a 1F capacitor charged to 1V. You have 2 2F caps, each with a charge of 1 coulomb, connected in series. Correct, which is a 1F capacitor charged to 1V for 1 coulomb. Repeat after me: coulombs in series are all the same as the whole. It MUST be so because the same current flows through each as the whole. Now, because Q = CV, and because charge is constant in an isolated system and you started with 2 coulombs charge, if you magically merged the two caps into a 1F cap, then Q=CV means that V would have to be 2, not 1. Doesn't bother you blowing conservation of energy to hell and back, eh? You've fallen for the 'add' diversion. Coulombs DO NOT ADD in series, just as amp/hours of batteries do not add in series. Volts do. It doesn't matter if you "magically merged" the two or connect them in series. The result is 1V on 1F for 1 coulomb. Repeat after me: coulombs in series are all the same as the whole. It MUST be so because the same current flows through each as the whole. Charge must be conserved. You are confusing your 'charges' (which, you may have noticed, is why I usually put the word in tic marks often with an 'explanation' like (Q) immediately following). A capacitor stores energy. When 'charging' (or 'discharging') the (ideal) capacitor an electron enters one plate and another electron exits the other (required by, guess what, conservation of charge). The 'charges' (electrons, holes) are rearranged, with equal - and + 'charges' on opposing plates, but the NET charge (0) is unchanged. There is no 'problem' conserving 0 whether you 'add', or not, and 0 + 0 is pretty much the same as 0 = 0. Close enough for government work anyway. Energy (.5CV^2) is a different matter, of course, and total E = .5J better be the case no matter how they're connected or else the universe will fold up into a reverse black hole (joke). Which is a serious problem for your two .5V 2F caps each with E = .25J, total E=.5J, merging in series to a 2V 1F cap with E = 2J. AAAAAaaaaeeeeee-------..... help me Quick, quick. It's really, just like the equations say, 1V on 1F for 1 coulomb and E= .5J ......-------eeeeeeaaaaAAAAA that's better. As I used "volume", those two caps occupy different cordinates, You see anything about "coordinates" in CV? No. It's irrelevant. they are not the magical merger the puzzle implies into a 1F cap, Yes they are. 1/Cs = 1/Ca + 1/Cb. It's a measurable fact. Live it and love it. and they must be considered as such: 2 separate capacitors, not a single 1F capacitor. Nonsense. I give you two leads. You stick a capacitance meter on them and it reads 1F. Now you tell me how many capacitors and in what arrangement I used to make up the 1F you just measured. Hint: No matter what you pick I'll claim it's another arrangement because it DOES NOT MATTER. Farads are Farads. Different volumes, no merger of coordinates, no merger of capacity. There's no current in or out of either cap. It simply does not matter, in the isolated system, that the total series capacitance would equal 1F in a non isolated system. And what magical transformation do you imagine takes place with the "not a 1F capacitor" when I stick a capacitance meter on them and measure 1F? The misdirection seems to me to be in the monkeying around with the volumes. Nope. The misdirection is in thinking coulombs 'must add' no matter how the caps are connected. Repeat after me: coulombs in series are all the same as the whole. It MUST be so because the same current flows through each as the whole. It states that you have a 1F cap. You do. 1/Cs = 1/Ca + 1/Cb. It's a measurable fact. Live it and love it. In fact you don't even have the equivalent of a 1F cap. Then, if not 1F, show me your 'volume' equations for what they 'really are' in series. You can't because they ARE 1F in series. The fact that you have 2 2F caps with an equivalent of a single 1F *if connected in series in a circuit* becomes important when you make the system no longer isolated by discharging. What 'magical transformation' are you expecting to happen? Do 'missing coulombs' mysteriously pop in or out? But the puzzle does *not* "un-isolate" the system. No current flows. Which is why they still have the charge. The serial caps are just two caps, each of which has one of its leads connected to the other cap, and its other lead floating free. There is no circuit. Those two caps might just as well be lying in your parts drawer. There is no equivalent capacitance. And what 'magical' transformation are you expecting to happen when one puts a capacitance meter on them and they measure 1F in series? Ed I can't begin to capture the whole metadiscussion, which spans several subjects and 2 (or more?) newsgroups, but at least I can quote the part where John posted the puzzle: Quoting from John Larkin's post, 7/10/2010 at 11:16 AM on SED. Subject: Win Hill: Inverse Marx Generator ?? To celebrate the 21st century, I have composed a new riddle: Start with a 4 farad cap charged to 0.5 volts. Q = 2 coulombs. Carefully saw it in half, without discharging it, such as to have two caps, each 2 farads, each charged to 0.5 volts. The total charge of the two caps remains 2 coulombs, whether you connect them in parallel or consider them separately. Now stack them in series. The result is a 1F cap charged to 1 volt. That has a charge of 1 coulomb. Where did the other coulomb go? I think this is a better riddle. Your rendition seems perfectly fine to me and there is no different mystery, or any mystery at all. As I said, you fell for the 'add' diversion. You have two 2F capacitors charged to .5V and take, hook, line and sinker, 1+1 coulombs as gospel no matter how they're connected so why do you not think volts 'must add' no matter how they're connected? I.E. If you're so perplexed by there being only 1 coulomb in the series 1F capacitor then why are you not perplexed there is only .5V on the parallel 4F capacitor (or that the 'sum' of the volts on the two 2s is twice what was there in parallel)? I'll wager it's because you know that volts do not add in parallel so why is it so darn hard for you to grasp that coulombs do not add in series? There is no '1 + 1 missing coulomb' in series any more than there is a 'missing .5V' when connected in parallel, nor any magical transformations needed to explain why nothings missing, because, repeat after me: coulombs in series are all the same as the whole. It MUST be so because the same current flows through each as the whole. I gave you the equations and you simply refuse to accept simple math. Coulombs is CV. You see anything other than C and V in that equation? No. .5V x 2F = 1 coulomb Put two of them in series and you have 1/Cs = 1/Ca + 1/Cb: 1F Vs = Va + Vb: 1V 1V x 1F = 1 coulomb. Those are all measurable FACTS. There is no "1 + 1" mystery because coulombs DO NOT ADD in series, just as volts do not add in parallel. Coulombs (current): series: same. Volts (potential): parallel: same. Get it? Note that those equations do not contain, nor does it matter, HOW the capacitors got there nor what 'volume' they are, nor how they're made, nor how many plates they have, nor how many capacitors make them up, nor what the dielectric is, nor how they were charged, nor what 'coordinates' you magically assign them, nor anything else: Charge them in parallel, charge them in series, charge them singly, charge them with a iPod, charge them with a lighting bolt from Thor the thunder god. Leave them in circuit, take them out of circuit, 'isolate' them, or don't. It DOES NOT MATTER. .5V on 2F is 1 coulomb and 1V on 1F is 1 coulomb; and that's true whether it's 'one' capacitor, of any form, or any number of capacitors or plates in any combination of series and parallel connections that comes to the stated Volts and Farads. That's all there is and there ain't no more. It amazes me how much effort you take, to try and get that penny to move just a little, for JF to realise his Aha! moment... I don't have your patience at all. Grant. John Maybe that is not the intended misdirection, but you and I can't get past the point of agreeing on what volume means. Really. Where did I ever dispute the meaning of 'volume'? A coulomb does not have the property of volume or mass. And volume or mass does not have the property of charge, spin, or color. So what? You act as if the only 'real' things in the universe are volume and mass so that all else are "only numbers;" and mysterious magical ones that invisibly 'change' when nothing else has. Whatever object has been charged does but the coulomb itself is just a number. And volume is "just a number." Volume is the product of measurable quantities. Coulombs is the product of measurable quantities. We can measure volume. We can measure coulombs. There is no mysticism involved. I'm sorry if that is a repeat, but it is a fact you don't agree to. We can't get any further. You can't go any further because you can't put any math to your 'volume' theory, which means you have not solved the 'puzzle' as arm waving about unexplained 'volume effects' does not solve equations. I do need to correct 2 points you made below: "You introduced the 'parallel to series' puzzle and I think I am the only one in this thread, so far, to explain it." Do not lay that puzzle at my doorstep! :-) (Well, unless you want to stomp on it. Even then attribute "ownership" where it belongs. :-) ) I didn't say you invented or 'owned' it. I said you introduced it here. John introduced the parallel to series puzzle elsewhere. If you say so. I attributed it to him in my post. And it's clear from the context that I'm talking about what someone else posted. Terrific. And thank you for introducing it to us. "That was John Larkin and he was neither the OP nor did he posit either of the 'puzzles'." He posted the 'parallel to series' puzzle on SED - obviously you missed it. This isn't SED, it's ABSE. In any event, it is not *my* puzzle, and I didn't pose it. I didn't say either. All I said is you introduced it. Good Lord, you act as if mentioning it is a heinous crime you plead not guilty to. Ed Changing the area/spacing ratios would, indeed, change the capacitance but it's irrelevant as the physical parameters are subsumed into the given capacitances and further irrelevant as none of the parameters change anyway. To go further. A coulomb is a numerical result of a mathematical operation, not a physical object. There is no physical object that is an "ampere second". A coulomb is massless, and volumeless. The puzzle misdirection appeared to be treating the coulomb as an object that could be divided by dividing that coulomb's container. It can. As you yourself pointed out, the story might as well begin with two 2s in parallel and skip the fluff of 'splitting' the 4 in half as the result is the same and nothing mysterious happens. You have two 2F capacitors each with a 'charge' (Q) of 1 coulomb. And as I pointed out, the entire parallel step is entirely superfluous as you have the same supposed 'mystery' if you just look at two 2's in series. Each have 1 coulomb and the total has one coulomb. Of course, as I also explained, there is no 'mystery' because coulombs do not add in series. They each and all have the same Q as the whole because the exact same current goes through each and all as the whole. I.E. instead of the 'mystery' posited by the diversion 1 + 1 = 1, "huh where's the missing coulomb?" the correct answer is 1 = 1 = 1, just as it should. Area and spacing, which define a volume, the dielectric of the volume and the applied volts determine the coulombs. It's not an 'arbitrary' thing and, in that sense, yes it is 'fixed' (by the particulars). Otherwise one would not be able to write an equation for it. It's even more the case when simply alternating between parallel or series connections as none of their parameters change, not even V (hence Q), and that's about as 'fixed' as one can get. which seems to be the misconception at the heart of the so called puzzle. If you are referring to the, so called, 'missing coulomb' there isn't one. Correct, there is no missing coulomb. I've already said that, earlier in the discussion. Ok. So I threaded back and, unless I misunderstood, you seem to be suggesting there is some unexplained 'difference' between whatever you deem a 'real' 1F capacitor and two 2s in series, despite their identical behavior, so that two 2s in series are "not a 1F cap" and 1F "doesn't matter." Not what I was suggesting. Ok. Then what did the two 2s are "not a 1F cap" and 1F "doesn't matter" mean? In the puzzle the 2 coulombs is a number that tells you how much current got stuffed into a container and how long the "stuffing" took. Magically dividing the container into two containers (or N containers) does not change the amount of current got stuffed in, nor the amount of time it took to do that stuffing. Exactly. So what is the machination on "volume" about? There's no need for mysterious 'differences' as, assuming all else is equal, a single 1F, two 2s in series, four 4s in series, eight 8s in series, and so on (although equal values are not required, just that the resulting series comes to 1F), are black box indistinguishable. At 1V overall they'll each and every one have 1 coulomb because they all have the exact same charging current go through. The puzzle's magic division creates the "mysterious differences" (it results in Vcap = V/N for each cap), Not so. Capacitors in parallel have the same V and still do when then 'disconnected' from each other (since they're 'ideal' with no leakage).. hiding the fact that total ampere seconds is the same. There's nothing 'hidden' about 2 parallel coulombs divided into two being 1 coulomb each. Albeit superfluous the parallel step is entirely accurate. You begin with .5V on 4F for 2 coulombs and you end up with two 2s each with .5V and 1 coulomb. 'Volume', dielectric, and all other physical parameters are irrelevant as they are subsumed into the 'given' capacitances. It doesn't matter how they are made as 2F is 2F. In parallel it's 4F and in series it's 1F. That's it. You may have missed the context of the whole starting from the beginning, when a "puzzle" (which wasn't a puzzle at all) was presented. Paul Hovnanian started the thread with a proposed 'solution' to the 'cap charging a cap' puzzle and mine was the first reply. All I did was point out that the 'solution' was equivalent to the oft posited voltage source charging an 'ideal' cap 'puzzle' and that substituting a cap for the voltage source simply makes the puzzle appear more mysterious than it is. (A sub thread then ensued about R=0) You introduced the 'parallel to series' puzzle and I think I am the only one in this thread, so far, to explain it. And I don't think it matters - the puzzle was just "mental gymnastics" that caused confusion instead of making a point, in my opinion. The purpose of a 'puzzle' is to posit what appears to be a conundrum for the reader to then figure out. The 'mystery' of the original puzzle is in leaving series R out of the model and the 'mystery' of the second is being diverted into thinking coulombs should 'add' when, in series, they do not. Your paragraph above shows you understand the principle, so the puzzle is irrelevant. And the op clarified his meaning: "My point all along is that, in actual circuit design, the generalism "charge is conserved" is dangerous, given that "charge" is ampere-seconds that you can actually measure and use." His "puzzle" was misdirection to show that a coulomb was somehow lost. No coulomb was lost. That was John Larkin and he was neither the OP nor did he posit either of the 'puzzles'. His first entry was to me and I did not respond because he hacked my words to imply I said things I did not and changed the model to boot so it wasn't even relevant to the discussion. Perhaps what I've posted isn't clear to you, but if you think that no coulomb was lost in the puzzle, and that a coulomb of charge does not require one and only one specific volume, then we're in agreement. You still seem to be positing some 'mysterious' thing about 'volume' that has nothing to do with solving the puzzle. Maybe if you put it to numbers I could gather what you mean. Here's my math Q(Coulombs) = CV, E(Joules) = .5QV (or, by substitution, .5CV^2) Each: 2F, .5V, 1C, .25J Parallel: 2F + 2F = 4F, .5V = .5V = .5V, 1C + 1C = 2C, .5J Series: 1/(1/2F + 1/2F) = 1F, .5V + .5V = 1V, 1C = 1C = 1C, .5J Note that 'Q per volume' (whatever it might be) of the 2F caps remains 'fixed' because neither Q nor 'volume' change and neither does V, or anything else. Or at least we can chose to 'pick' that simpler case because 'volume' is not mentioned anywhere since, being subsumed into F, it's completely irrelevant. Energy is conserved, 'charge' (Q) is conserved, and all is right with the world. There is no 'puzzle' unless one is fooled by the riddle into thinking series coulombs should add. Ed Ed snip |
#22
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
On Tue, 27 Jul 2010 13:10:45 +1000, Grant wrote:
On Mon, 26 Jul 2010 15:59:32 -0700, Jim Thompson wrote: ... Populated Only by Bloviators and Pompous PhD's Here I was, thinking you made that word up, so google found for me: " According to WikiPedia, to bloviate is to "speak pompously and excessively", or "to expound ridiculously". A colloquial verb coined in the United States, it is commonly used with contempt to describe the behavior of politicians, academics, pundits or media "experts", sometimes called bloviators, who hold forth on subjects in an arrogant, tiresome way. " -- http://www.bloviators.net/ There, they have their very own website! Grant. The only words I "make up" are shortenings of long silent letter words like changing "through" to "thru" and creating acoustic expletives like "Naaaah" :-) ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | Spice is like a sports car... Performance only as good as the person behind the wheel. |
#23
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
On Tue, 27 Jul 2010 00:22:36 -0500, flipper wrote:
On Mon, 26 Jul 2010 15:53:21 -0700, Jim Thompson wrote: On Mon, 26 Jul 2010 15:37:12 -0500, flipper wrote: On Mon, 26 Jul 2010 07:57:11 -0700, Jim Thompson wrote: On Mon, 26 Jul 2010 00:33:58 -0500, flipper wrote: On Sun, 25 Jul 2010 21:31:45 -0700, Jim Thompson wrote: [snip] "Ivor Catt" sounds like I should know him... '50's, early '60's ??? Well, the wikipedia article says he was born in 1935 so that would make him around 75. ...Jim Thompson I was talking of the year-range where I think I met him... possibly at Motorola. With a name like that, one rarely forgets :-) Oh. Well, how in the world would I know THAT? LOL I do see references to him at Motorola. One says 'mid' 1960s and the other said 'late' 1960s. I also see 1964 and 1966 referenced in some papers. ...Jim Thompson OK. I was Moto from 6/62 to 11/70 Ah. Well, then you very well might have met the Ivor. ...Jim Thompson Like I said, I'm sure I did... how could you possibly forget a name like that ?:-) ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | Spice is like a sports car... Performance only as good as the person behind the wheel. |
#24
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
flipper wrote:
You have totally missed it, either because you just want to argue, or because you don't recognize or don't understand conservation of charge. The puzzle starts with a cap with a charge of 2 coulombs. You claim the end result is one coulomb. Where is the external connection, to remove charge? The puzzle does not mention one. "The Law of Conservation of Charge The net charge of an isolated system remains constant. The only way to change the net charge of a system is to bring in charge from elsewhere, or remove charge from the system. " http://physics.bu.edu/~duffy/semeste...servation.html Argue with them, if you want. Ed On Mon, 26 Jul 2010 18:03:11 -0400, ehsjr wrote: flipper wrote: much snipped Where you claim the 'puzzle' lies, 'splitting' the 4F into two 2s, there's no puzzle at all. That is not what I said at all. I have no problem with magically cutting the 4F charged to .5 volts and Q=2cap into 2 2F caps each charged to .5 volts with Q=1 for each cap, as the puzzle proposes. Terrific. As I explained, you have the ENTIRE 'puzzle' if you just put two 2s in series and charge them up to 1V. Ok, _now_ I see what you are missing. That is most definitely NOT in the puzzle. The caps were not *charged* in series. You missed what the puzzle says. No, I did not 'miss' what the puzzle says. It's irrelevant as it makes NO difference if you 'charge' them in parallel, in series, or separately. The math is IDENTICAL, which is why I explained that the parallel step is superfluous and you might as well start with them in series. You have EXACTLY the same situation. Both 2F capacitors have 1 coulomb and the whole 1F capacitor has one coulomb. 1 + 1 = 1. Where is the missing coulomb? I don't understand your point above - I'm guessing that you're indicating that coulombs don't add. That's right. Coulombs do not add in series. But you are referring to the wrong scenario, in any event. No I am not. It is the exact same "scenario" as it does not matter 'how' 1 coulomb gets in the 2F cap. .5V on 2F is 1 coulomb is 1 coulomb is 1 coulomb. Put the two 2s in parallel, charge them to .5V, and you have 1 coulomb on each. Charge them in series to 1V overall and you have 1 coulomb on each. Charge them separately to .5V and you have 1 coulomb on each. It DOES NOT MATTER. 1 coulomb is 1 coulomb is 1 coulomb. Not ONE thing 'changes'. They are completely static with not even a connection change. Explain that one with your 'volumes'. Don't be absurd. The puzzle stipulates changes. Nope. The 2F caps have .5V for 1 coulomb throughout the entire exercise. NOTHING about the capacitors and their charge changes. The only misdirection is in thinking coulombs add in series when they don't. Here http://farside.ph.utexas.edu/teachin...es/node46.html Two capacitors connected in series. "... the fact that the charge is common to all three capacitors. " Your cite above refers to a non-isolated system. Oh? And just what are the bare wires sticking out each end 'connected' to? Doesn't matter anyway. Volts are Volts and Farads are Farads. You jumped into the middle of an ongoing metadiscussion that started on SED, so you are not aware of what has gone before. There was a large amount of discussion on conservation of charge, and it spanned more than one subject. JL made the point that charge is sometimes not conserved. Doesn't matter what went on before. Capacitors can't read nor do they care what sense or nonsense someone wrote. I'll cut and paste the puzzle as he wrote it, below my comments. His puzzle takes an isolated system, that starts out *already* charged with 2 coulombs, and monkeys around with the volumes inside the system. Your cite above refers to a non isolated system, and is not applicable to an isolated system. You see any reference to 'volumes' in CV? No. It's irrelevant. If you don't like the use of the word volume, fine. Substitute whatever term you want that includes the concept of the capacity of that volume and the coordinates that describe the place where your chosen term exists. Or use whatever term(s) that allow you to realize that 2 2F capacitors in series are NOT *a* 1F capacitor in the puzzle, without getting sidetracked into thinking that 1/Ct = 1/C1+1/C2...1/Cn applies to the isolated system. You, again, try to make hay from nonsense. Do you see anything in the equations that qualify 'how' a "1F capacitor" is 'made'? No. It doesn't matter if I use two plates or a hundred little plates in parallel or a dozen large plates in series or a combination. Farads are Farads. Two 2s in series ARE "a 1F capacitor" and 1/Ct = 1/C1+1/C2...1/Cn is not a 'sidetrack', it's a measurable fact. If it makes you feel any better then pot them in a tube with two leads sticking out. It's 1F. The law of conservation of charge applies as long as the system remains isolated. The number of coulombs remains constant, regardless of the volume (size, whatever your term is) of the pieces you magically slice the original cap into, or how you connect them, in that isolated system. The puzzle ends up stating that after the slicing & serial connecting, you have *a* 1F cap charged to 1 volt. That is *false*. It is perfectly true. You DO have a 1F capacitor charged to 1V. You have 2 2F caps, each with a charge of 1 coulomb, connected in series. Correct, which is a 1F capacitor charged to 1V for 1 coulomb. Repeat after me: coulombs in series are all the same as the whole. It MUST be so because the same current flows through each as the whole. Now, because Q = CV, and because charge is constant in an isolated system and you started with 2 coulombs charge, if you magically merged the two caps into a 1F cap, then Q=CV means that V would have to be 2, not 1. Doesn't bother you blowing conservation of energy to hell and back, eh? You've fallen for the 'add' diversion. Coulombs DO NOT ADD in series, just as amp/hours of batteries do not add in series. Volts do. It doesn't matter if you "magically merged" the two or connect them in series. The result is 1V on 1F for 1 coulomb. Repeat after me: coulombs in series are all the same as the whole. It MUST be so because the same current flows through each as the whole. Charge must be conserved. You are confusing your 'charges' (which, you may have noticed, is why I usually put the word in tic marks often with an 'explanation' like (Q) immediately following). A capacitor stores energy. When 'charging' (or 'discharging') the (ideal) capacitor an electron enters one plate and another electron exits the other (required by, guess what, conservation of charge). The 'charges' (electrons, holes) are rearranged, with equal - and + 'charges' on opposing plates, but the NET charge (0) is unchanged. There is no 'problem' conserving 0 whether you 'add', or not, and 0 + 0 is pretty much the same as 0 = 0. Close enough for government work anyway. Energy (.5CV^2) is a different matter, of course, and total E = .5J better be the case no matter how they're connected or else the universe will fold up into a reverse black hole (joke). Which is a serious problem for your two .5V 2F caps each with E = .25J, total E=.5J, merging in series to a 2V 1F cap with E = 2J. AAAAAaaaaeeeeee-------..... help me Quick, quick. It's really, just like the equations say, 1V on 1F for 1 coulomb and E= .5J ......-------eeeeeeaaaaAAAAA that's better. As I used "volume", those two caps occupy different cordinates, You see anything about "coordinates" in CV? No. It's irrelevant. they are not the magical merger the puzzle implies into a 1F cap, Yes they are. 1/Cs = 1/Ca + 1/Cb. It's a measurable fact. Live it and love it. and they must be considered as such: 2 separate capacitors, not a single 1F capacitor. Nonsense. I give you two leads. You stick a capacitance meter on them and it reads 1F. Now you tell me how many capacitors and in what arrangement I used to make up the 1F you just measured. Hint: No matter what you pick I'll claim it's another arrangement because it DOES NOT MATTER. Farads are Farads. Different volumes, no merger of coordinates, no merger of capacity. There's no current in or out of either cap. It simply does not matter, in the isolated system, that the total series capacitance would equal 1F in a non isolated system. And what magical transformation do you imagine takes place with the "not a 1F capacitor" when I stick a capacitance meter on them and measure 1F? The misdirection seems to me to be in the monkeying around with the volumes. Nope. The misdirection is in thinking coulombs 'must add' no matter how the caps are connected. Repeat after me: coulombs in series are all the same as the whole. It MUST be so because the same current flows through each as the whole. It states that you have a 1F cap. You do. 1/Cs = 1/Ca + 1/Cb. It's a measurable fact. Live it and love it. In fact you don't even have the equivalent of a 1F cap. Then, if not 1F, show me your 'volume' equations for what they 'really are' in series. You can't because they ARE 1F in series. The fact that you have 2 2F caps with an equivalent of a single 1F *if connected in series in a circuit* becomes important when you make the system no longer isolated by discharging. What 'magical transformation' are you expecting to happen? Do 'missing coulombs' mysteriously pop in or out? But the puzzle does *not* "un-isolate" the system. No current flows. Which is why they still have the charge. The serial caps are just two caps, each of which has one of its leads connected to the other cap, and its other lead floating free. There is no circuit. Those two caps might just as well be lying in your parts drawer. There is no equivalent capacitance. And what 'magical' transformation are you expecting to happen when one puts a capacitance meter on them and they measure 1F in series? Ed I can't begin to capture the whole metadiscussion, which spans several subjects and 2 (or more?) newsgroups, but at least I can quote the part where John posted the puzzle: Quoting from John Larkin's post, 7/10/2010 at 11:16 AM on SED. Subject: Win Hill: Inverse Marx Generator ?? To celebrate the 21st century, I have composed a new riddle: Start with a 4 farad cap charged to 0.5 volts. Q = 2 coulombs. Carefully saw it in half, without discharging it, such as to have two caps, each 2 farads, each charged to 0.5 volts. The total charge of the two caps remains 2 coulombs, whether you connect them in parallel or consider them separately. Now stack them in series. The result is a 1F cap charged to 1 volt. That has a charge of 1 coulomb. Where did the other coulomb go? I think this is a better riddle. Your rendition seems perfectly fine to me and there is no different mystery, or any mystery at all. As I said, you fell for the 'add' diversion. You have two 2F capacitors charged to .5V and take, hook, line and sinker, 1+1 coulombs as gospel no matter how they're connected so why do you not think volts 'must add' no matter how they're connected? I.E. If you're so perplexed by there being only 1 coulomb in the series 1F capacitor then why are you not perplexed there is only .5V on the parallel 4F capacitor (or that the 'sum' of the volts on the two 2s is twice what was there in parallel)? I'll wager it's because you know that volts do not add in parallel so why is it so darn hard for you to grasp that coulombs do not add in series? There is no '1 + 1 missing coulomb' in series any more than there is a 'missing .5V' when connected in parallel, nor any magical transformations needed to explain why nothings missing, because, repeat after me: coulombs in series are all the same as the whole. It MUST be so because the same current flows through each as the whole. I gave you the equations and you simply refuse to accept simple math. Coulombs is CV. You see anything other than C and V in that equation? No. .5V x 2F = 1 coulomb Put two of them in series and you have 1/Cs = 1/Ca + 1/Cb: 1F Vs = Va + Vb: 1V 1V x 1F = 1 coulomb. Those are all measurable FACTS. There is no "1 + 1" mystery because coulombs DO NOT ADD in series, just as volts do not add in parallel. Coulombs (current): series: same. Volts (potential): parallel: same. Get it? Note that those equations do not contain, nor does it matter, HOW the capacitors got there nor what 'volume' they are, nor how they're made, nor how many plates they have, nor how many capacitors make them up, nor what the dielectric is, nor how they were charged, nor what 'coordinates' you magically assign them, nor anything else: Charge them in parallel, charge them in series, charge them singly, charge them with a iPod, charge them with a lighting bolt from Thor the thunder god. Leave them in circuit, take them out of circuit, 'isolate' them, or don't. It DOES NOT MATTER. .5V on 2F is 1 coulomb and 1V on 1F is 1 coulomb; and that's true whether it's 'one' capacitor, of any form, or any number of capacitors or plates in any combination of series and parallel connections that comes to the stated Volts and Farads. That's all there is and there ain't no more. John Maybe that is not the intended misdirection, but you and I can't get past the point of agreeing on what volume means. Really. Where did I ever dispute the meaning of 'volume'? A coulomb does not have the property of volume or mass. And volume or mass does not have the property of charge, spin, or color. So what? You act as if the only 'real' things in the universe are volume and mass so that all else are "only numbers;" and mysterious magical ones that invisibly 'change' when nothing else has. Whatever object has been charged does but the coulomb itself is just a number. And volume is "just a number." Volume is the product of measurable quantities. Coulombs is the product of measurable quantities. We can measure volume. We can measure coulombs. There is no mysticism involved. I'm sorry if that is a repeat, but it is a fact you don't agree to. We can't get any further. You can't go any further because you can't put any math to your 'volume' theory, which means you have not solved the 'puzzle' as arm waving about unexplained 'volume effects' does not solve equations. I do need to correct 2 points you made below: "You introduced the 'parallel to series' puzzle and I think I am the only one in this thread, so far, to explain it." Do not lay that puzzle at my doorstep! :-) (Well, unless you want to stomp on it. Even then attribute "ownership" where it belongs. :-) ) I didn't say you invented or 'owned' it. I said you introduced it here. John introduced the parallel to series puzzle elsewhere. If you say so. I attributed it to him in my post. And it's clear from the context that I'm talking about what someone else posted. Terrific. And thank you for introducing it to us. "That was John Larkin and he was neither the OP nor did he posit either of the 'puzzles'." He posted the 'parallel to series' puzzle on SED - obviously you missed it. This isn't SED, it's ABSE. In any event, it is not *my* puzzle, and I didn't pose it. I didn't say either. All I said is you introduced it. Good Lord, you act as if mentioning it is a heinous crime you plead not guilty to. Ed Changing the area/spacing ratios would, indeed, change the capacitance but it's irrelevant as the physical parameters are subsumed into the given capacitances and further irrelevant as none of the parameters change anyway. To go further. A coulomb is a numerical result of a mathematical operation, not a physical object. There is no physical object that is an "ampere second". A coulomb is massless, and volumeless. The puzzle misdirection appeared to be treating the coulomb as an object that could be divided by dividing that coulomb's container. It can. As you yourself pointed out, the story might as well begin with two 2s in parallel and skip the fluff of 'splitting' the 4 in half as the result is the same and nothing mysterious happens. You have two 2F capacitors each with a 'charge' (Q) of 1 coulomb. And as I pointed out, the entire parallel step is entirely superfluous as you have the same supposed 'mystery' if you just look at two 2's in series. Each have 1 coulomb and the total has one coulomb. Of course, as I also explained, there is no 'mystery' because coulombs do not add in series. They each and all have the same Q as the whole because the exact same current goes through each and all as the whole. I.E. instead of the 'mystery' posited by the diversion 1 + 1 = 1, "huh where's the missing coulomb?" the correct answer is 1 = 1 = 1, just as it should. Area and spacing, which define a volume, the dielectric of the volume and the applied volts determine the coulombs. It's not an 'arbitrary' thing and, in that sense, yes it is 'fixed' (by the particulars). Otherwise one would not be able to write an equation for it. It's even more the case when simply alternating between parallel or series connections as none of their parameters change, not even V (hence Q), and that's about as 'fixed' as one can get. which seems to be the misconception at the heart of the so called puzzle. If you are referring to the, so called, 'missing coulomb' there isn't one. Correct, there is no missing coulomb. I've already said that, earlier in the discussion. Ok. So I threaded back and, unless I misunderstood, you seem to be suggesting there is some unexplained 'difference' between whatever you deem a 'real' 1F capacitor and two 2s in series, despite their identical behavior, so that two 2s in series are "not a 1F cap" and 1F "doesn't matter." Not what I was suggesting. Ok. Then what did the two 2s are "not a 1F cap" and 1F "doesn't matter" mean? In the puzzle the 2 coulombs is a number that tells you how much current got stuffed into a container and how long the "stuffing" took. Magically dividing the container into two containers (or N containers) does not change the amount of current got stuffed in, nor the amount of time it took to do that stuffing. Exactly. So what is the machination on "volume" about? There's no need for mysterious 'differences' as, assuming all else is equal, a single 1F, two 2s in series, four 4s in series, eight 8s in series, and so on (although equal values are not required, just that the resulting series comes to 1F), are black box indistinguishable. At 1V overall they'll each and every one have 1 coulomb because they all have the exact same charging current go through. The puzzle's magic division creates the "mysterious differences" (it results in Vcap = V/N for each cap), Not so. Capacitors in parallel have the same V and still do when then 'disconnected' from each other (since they're 'ideal' with no leakage).. hiding the fact that total ampere seconds is the same. There's nothing 'hidden' about 2 parallel coulombs divided into two being 1 coulomb each. Albeit superfluous the parallel step is entirely accurate. You begin with .5V on 4F for 2 coulombs and you end up with two 2s each with .5V and 1 coulomb. 'Volume', dielectric, and all other physical parameters are irrelevant as they are subsumed into the 'given' capacitances. It doesn't matter how they are made as 2F is 2F. In parallel it's 4F and in series it's 1F. That's it. You may have missed the context of the whole starting from the beginning, when a "puzzle" (which wasn't a puzzle at all) was presented. Paul Hovnanian started the thread with a proposed 'solution' to the 'cap charging a cap' puzzle and mine was the first reply. All I did was point out that the 'solution' was equivalent to the oft posited voltage source charging an 'ideal' cap 'puzzle' and that substituting a cap for the voltage source simply makes the puzzle appear more mysterious than it is. (A sub thread then ensued about R=0) You introduced the 'parallel to series' puzzle and I think I am the only one in this thread, so far, to explain it. And I don't think it matters - the puzzle was just "mental gymnastics" that caused confusion instead of making a point, in my opinion. The purpose of a 'puzzle' is to posit what appears to be a conundrum for the reader to then figure out. The 'mystery' of the original puzzle is in leaving series R out of the model and the 'mystery' of the second is being diverted into thinking coulombs should 'add' when, in series, they do not. Your paragraph above shows you understand the principle, so the puzzle is irrelevant. And the op clarified his meaning: "My point all along is that, in actual circuit design, the generalism "charge is conserved" is dangerous, given that "charge" is ampere-seconds that you can actually measure and use." His "puzzle" was misdirection to show that a coulomb was somehow lost. No coulomb was lost. That was John Larkin and he was neither the OP nor did he posit either of the 'puzzles'. His first entry was to me and I did not respond because he hacked my words to imply I said things I did not and changed the model to boot so it wasn't even relevant to the discussion. Perhaps what I've posted isn't clear to you, but if you think that no coulomb was lost in the puzzle, and that a coulomb of charge does not require one and only one specific volume, then we're in agreement. You still seem to be positing some 'mysterious' thing about 'volume' that has nothing to do with solving the puzzle. Maybe if you put it to numbers I could gather what you mean. Here's my math Q(Coulombs) = CV, E(Joules) = .5QV (or, by substitution, .5CV^2) Each: 2F, .5V, 1C, .25J Parallel: 2F + 2F = 4F, .5V = .5V = .5V, 1C + 1C = 2C, .5J Series: 1/(1/2F + 1/2F) = 1F, .5V + .5V = 1V, 1C = 1C = 1C, .5J Note that 'Q per volume' (whatever it might be) of the 2F caps remains 'fixed' because neither Q nor 'volume' change and neither does V, or anything else. Or at least we can chose to 'pick' that simpler case because 'volume' is not mentioned anywhere since, being subsumed into F, it's completely irrelevant. Energy is conserved, 'charge' (Q) is conserved, and all is right with the world. There is no 'puzzle' unless one is fooled by the riddle into thinking series coulombs should add. Ed Ed snip |
#25
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
On Tue, 27 Jul 2010 11:28:14 -0400, ehsjr
wrote: flipper wrote: You have totally missed it, either because you just want to argue, or because you don't recognize or don't understand conservation of charge. The puzzle starts with a cap with a charge of 2 coulombs. You claim the end result is one coulomb. Where is the external connection, to remove charge? The puzzle does not mention one. "The Law of Conservation of Charge The net charge of an isolated system remains constant. The only way to change the net charge of a system is to bring in charge from elsewhere, or remove charge from the system. " http://physics.bu.edu/~duffy/semeste...servation.html Argue with them, if you want. Ed [snip] Absolutely correct... Only YOU can prevent forest fires. but only "The Bloviator" can destroy charge or create non-conservation events :-) ...Jim Thompson -- | James E.Thompson, CTO | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona 85048 Skype: Contacts Only | | | Voice480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | SED Has Crumbled to Below SEB Status Populated Only by Bloviators and Pompous PhD's |
#26
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
On Tue, 27 Jul 2010 07:33:21 -0500, flipper wrote:
On Tue, 27 Jul 2010 19:50:51 +1000, Grant wrote: On Tue, 27 Jul 2010 00:21:20 -0500, flipper wrote: snip It amazes me how much effort you take, to try and get that penny to move just a little, for JF to realise his Aha! moment... That really would make it worthwhile, wouldn't it? To help out an Aha! moment. Yes, it's truly wonderful to see the penny drop To help another get there too, is good. Besides, I had a bit of fun with magical coulombs and reverse black holes Adding a bit of fun can help at times too, maybe break that 'eyes glazed over' look which I saw way too often when I was trying to explain my ideas. Grant. |
#27
Posted to alt.binaries.schematics.electronic
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Two Cap Puzzle
flipper wrote:
On Sat, 24 Jul 2010 17:31:57 +0100, "Ian" wrote: "Jim Thompson" wrote in message ... I'm trying to write it up, both I keep getting interrupted by work that pays $:-) ...Jim Thompson I'd be interested to see your write up, Jim. This conundrum was asked of me in a pre-uni interview more than 40 years ago, I forget my real answer, I think I doubted the assumption of zero resistance. There were some wacky claims by (I think it was) Ivor Catt in a discussion on this in Wireless World where he claimed it proved the existence of some wonderful new thingy ("displacement current"?). Much sound and fury, but little edification ensued as I recall. I should see if I still have the letters. My understanding is that Ivor Catt doesn't believe in displacement current or much else of conventional electromagnetism. http://en.wikipedia.org/wiki/Ivor_Catt http://en.wikipedia.org/wiki/Displacement_current It did cause me to be wary of "stated conditions" aka basic assumptions in engineering problems in later life ;-) A wise caution. Regards Ian Of course, if there's no displacement current, there are no electromagnetic waves, proving that Ivor Catt (whoever he is) can't see his own shadow. Moving on. Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal ElectroOptical Innovations 55 Orchard Rd Briarcliff Manor NY 10510 845-480-2058 hobbs at electrooptical dot net http://electrooptical.net |
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