Series, parallel, and series-parallel resistors - series parallel R.pdf
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Series, parallel, and series-parallel resistors - series parallel R.pdf
On Fri, 21 Oct 2011 08:54:15 -0500, John Fields
wrote: -- JF |
Series, parallel, and series-parallel resistors - series parallelR.pdf
John Fields wrote:
A nice PDF. I like it - much better than the text output my program produces (shown below). I programmed it, using the 18 ohm resistors mentioned in the original post. Total R is shown in the right hand column. I like it better your way, with the schematic and the generic R. It works works for any value of R; my program does too, but the output is limited to only one resistor value per run. Your multiplication factor works for any resistance. Here's the output I got: 10 in parallel = 1.8 9 in parallel = 2 8 in parallel = 2.25 7 in parallel = 2.57142857 6 in parallel = 3 5 in parallel = 3.6 4 in parallel = 4.5 3 in parallel = 6 2 in parallel = 9 1 single resistor = 18 1 in series with 9 in parallel = 20 1 in series with 8 in parallel = 20.25 1 in series with 7 in parallel = 20.5714286 1 in series with 6 in parallel = 21 1 in series with 5 in parallel = 21.6 1 in series with 4 in parallel = 22.5 1 in series with 3 in parallel = 24 1 in series with 2 in parallel = 27 1 in series with 1 in parallel = 36 2 in series with 8 in parallel = 38.25 2 in series with 7 in parallel = 38.5714286 2 in series with 6 in parallel = 39 2 in series with 5 in parallel = 39.6 2 in series with 4 in parallel = 40.5 2 in series with 3 in parallel = 42 2 in series with 2 in parallel = 45 2 in series with 1 in parallel = 54 3 in series with 7 in parallel = 56.5714286 3 in series with 6 in parallel = 57 3 in series with 5 in parallel = 57.6 3 in series with 4 in parallel = 58.5 3 in series with 3 in parallel = 60 3 in series with 2 in parallel = 63 3 in series with 1 in parallel = 72 4 in series with 6 in parallel = 75 4 in series with 5 in parallel = 75.6 4 in series with 4 in parallel = 76.5 4 in series with 3 in parallel = 78 4 in series with 2 in parallel = 81 4 in series with 1 in parallel = 90 5 in series with 5 in parallel = 93.6 5 in series with 4 in parallel = 94.5 5 in series with 3 in parallel = 96 5 in series with 2 in parallel = 99 5 in series with 1 in parallel = 108 6 in series with 4 in parallel = 112.5 6 in series with 3 in parallel = 114 6 in series with 2 in parallel = 117 6 in series with 1 in parallel = 126 7 in series with 3 in parallel = 132 7 in series with 2 in parallel = 135 7 in series with 1 in parallel = 144 8 in series with 2 in parallel = 153 8 in series with 1 in parallel = 162 9 in series with 1 in parallel = 180 Ed |
Series, parallel, and series-parallel resistors - series parallel R.pdf
On Sat, 22 Oct 2011 02:12:11 -0400, ehsjr
wrote: John Fields wrote: A nice PDF. I like it - much better than the text output my program produces (shown below). I programmed it, using the 18 ohm resistors mentioned in the original post. Total R is shown in the right hand column. I like it better your way, with the schematic and the generic R. It works works for any value of R; my program does too, but the output is limited to only one resistor value per run. Your multiplication factor works for any resistance. Here's the output I got: 10 in parallel = 1.8 9 in parallel = 2 8 in parallel = 2.25 7 in parallel = 2.57142857 6 in parallel = 3 5 in parallel = 3.6 4 in parallel = 4.5 3 in parallel = 6 2 in parallel = 9 1 single resistor = 18 1 in series with 9 in parallel = 20 1 in series with 8 in parallel = 20.25 1 in series with 7 in parallel = 20.5714286 1 in series with 6 in parallel = 21 1 in series with 5 in parallel = 21.6 1 in series with 4 in parallel = 22.5 1 in series with 3 in parallel = 24 1 in series with 2 in parallel = 27 1 in series with 1 in parallel = 36 2 in series with 8 in parallel = 38.25 2 in series with 7 in parallel = 38.5714286 2 in series with 6 in parallel = 39 2 in series with 5 in parallel = 39.6 2 in series with 4 in parallel = 40.5 2 in series with 3 in parallel = 42 2 in series with 2 in parallel = 45 2 in series with 1 in parallel = 54 3 in series with 7 in parallel = 56.5714286 3 in series with 6 in parallel = 57 3 in series with 5 in parallel = 57.6 3 in series with 4 in parallel = 58.5 3 in series with 3 in parallel = 60 3 in series with 2 in parallel = 63 3 in series with 1 in parallel = 72 4 in series with 6 in parallel = 75 4 in series with 5 in parallel = 75.6 4 in series with 4 in parallel = 76.5 4 in series with 3 in parallel = 78 4 in series with 2 in parallel = 81 4 in series with 1 in parallel = 90 5 in series with 5 in parallel = 93.6 5 in series with 4 in parallel = 94.5 5 in series with 3 in parallel = 96 5 in series with 2 in parallel = 99 5 in series with 1 in parallel = 108 6 in series with 4 in parallel = 112.5 6 in series with 3 in parallel = 114 6 in series with 2 in parallel = 117 6 in series with 1 in parallel = 126 7 in series with 3 in parallel = 132 7 in series with 2 in parallel = 135 7 in series with 1 in parallel = 144 8 in series with 2 in parallel = 153 8 in series with 1 in parallel = 162 9 in series with 1 in parallel = 180 --- Nicely done, and thanks for the kind words. :-) -- JF |
Series, parallel, and series-parallel resistors - series parallel R.pdf
"ehsjr" wrote in message ... John Fields wrote: A nice PDF. I like it - much better than the text output my program produces (shown below). I programmed it, using the 18 ohm resistors mentioned in the original post. Total R is shown in the right hand column. I like it better your way, with the schematic and the generic R. It works works for any value of R; my program does too, but the output is limited to only one resistor value per run. Your multiplication factor works for any resistance. Here's the output I got: 10 in parallel = 1.8 9 in parallel = 2 8 in parallel = 2.25 7 in parallel = 2.57142857 6 in parallel = 3 5 in parallel = 3.6 4 in parallel = 4.5 3 in parallel = 6 2 in parallel = 9 1 single resistor = 18 1 in series with 9 in parallel = 20 1 in series with 8 in parallel = 20.25 1 in series with 7 in parallel = 20.5714286 1 in series with 6 in parallel = 21 1 in series with 5 in parallel = 21.6 1 in series with 4 in parallel = 22.5 1 in series with 3 in parallel = 24 1 in series with 2 in parallel = 27 1 in series with 1 in parallel = 36 2 in series with 8 in parallel = 38.25 2 in series with 7 in parallel = 38.5714286 2 in series with 6 in parallel = 39 2 in series with 5 in parallel = 39.6 2 in series with 4 in parallel = 40.5 2 in series with 3 in parallel = 42 2 in series with 2 in parallel = 45 2 in series with 1 in parallel = 54 3 in series with 7 in parallel = 56.5714286 3 in series with 6 in parallel = 57 3 in series with 5 in parallel = 57.6 3 in series with 4 in parallel = 58.5 3 in series with 3 in parallel = 60 3 in series with 2 in parallel = 63 3 in series with 1 in parallel = 72 4 in series with 6 in parallel = 75 4 in series with 5 in parallel = 75.6 4 in series with 4 in parallel = 76.5 4 in series with 3 in parallel = 78 4 in series with 2 in parallel = 81 4 in series with 1 in parallel = 90 5 in series with 5 in parallel = 93.6 5 in series with 4 in parallel = 94.5 5 in series with 3 in parallel = 96 5 in series with 2 in parallel = 99 5 in series with 1 in parallel = 108 6 in series with 4 in parallel = 112.5 6 in series with 3 in parallel = 114 6 in series with 2 in parallel = 117 6 in series with 1 in parallel = 126 7 in series with 3 in parallel = 132 7 in series with 2 in parallel = 135 7 in series with 1 in parallel = 144 8 in series with 2 in parallel = 153 8 in series with 1 in parallel = 162 9 in series with 1 in parallel = 180 Ed Maybe I'm missing what you and Ed are trying to show but per the OP it seems you both are missing some combinations such as 3P in series with 3P = 12ohms. Art |
Series, parallel, and series-parallel resistors - series parallel R.pdf
On Sat, 22 Oct 2011 18:33:18 -0700, "Artemus"
wrote: "ehsjr" wrote in message ... John Fields wrote: A nice PDF. I like it - much better than the text output my program produces (shown below). I programmed it, using the 18 ohm resistors mentioned in the original post. Total R is shown in the right hand column. I like it better your way, with the schematic and the generic R. It works works for any value of R; my program does too, but the output is limited to only one resistor value per run. Your multiplication factor works for any resistance. Here's the output I got: 10 in parallel = 1.8 9 in parallel = 2 8 in parallel = 2.25 7 in parallel = 2.57142857 6 in parallel = 3 5 in parallel = 3.6 4 in parallel = 4.5 3 in parallel = 6 2 in parallel = 9 1 single resistor = 18 1 in series with 9 in parallel = 20 1 in series with 8 in parallel = 20.25 1 in series with 7 in parallel = 20.5714286 1 in series with 6 in parallel = 21 1 in series with 5 in parallel = 21.6 1 in series with 4 in parallel = 22.5 1 in series with 3 in parallel = 24 1 in series with 2 in parallel = 27 1 in series with 1 in parallel = 36 2 in series with 8 in parallel = 38.25 2 in series with 7 in parallel = 38.5714286 2 in series with 6 in parallel = 39 2 in series with 5 in parallel = 39.6 2 in series with 4 in parallel = 40.5 2 in series with 3 in parallel = 42 2 in series with 2 in parallel = 45 2 in series with 1 in parallel = 54 3 in series with 7 in parallel = 56.5714286 3 in series with 6 in parallel = 57 3 in series with 5 in parallel = 57.6 3 in series with 4 in parallel = 58.5 3 in series with 3 in parallel = 60 3 in series with 2 in parallel = 63 3 in series with 1 in parallel = 72 4 in series with 6 in parallel = 75 4 in series with 5 in parallel = 75.6 4 in series with 4 in parallel = 76.5 4 in series with 3 in parallel = 78 4 in series with 2 in parallel = 81 4 in series with 1 in parallel = 90 5 in series with 5 in parallel = 93.6 5 in series with 4 in parallel = 94.5 5 in series with 3 in parallel = 96 5 in series with 2 in parallel = 99 5 in series with 1 in parallel = 108 6 in series with 4 in parallel = 112.5 6 in series with 3 in parallel = 114 6 in series with 2 in parallel = 117 6 in series with 1 in parallel = 126 7 in series with 3 in parallel = 132 7 in series with 2 in parallel = 135 7 in series with 1 in parallel = 144 8 in series with 2 in parallel = 153 8 in series with 1 in parallel = 162 9 in series with 1 in parallel = 180 Ed Maybe I'm missing what you and Ed are trying to show but per the OP it seems you both are missing some combinations such as 3P in series with 3P = 12ohms. Art There are a *lot* more combinations, like complex bridged stacks. I wonder if there is a general way to enumerate them all. John |
Series, parallel, and series-parallel resistors - series parallel R.pdf
On Sat, 22 Oct 2011 18:33:18 -0700, "Artemus"
wrote: Maybe I'm missing what you and Ed are trying to show but per the OP it seems you both are missing some combinations such as 3P in series with 3P = 12ohms. Art --- I was just trying to show the simplest set of series, parallel, and series-parallel connections available using from one to ten equal-valued resistors. There are, indeed, many more combinations available, one of them being the 3P in series with 3P: --+-[R1]-[R2]-[R3]-+--+-[R7]-[R8]-[R9]---+-- | | | | +-[R4]-[R5]-[R6]-+ +-[R10]-[R11]-[R12]+ but the end-to-end resistance isn't 12 ohms, it's: (R1+R2+R3)*(R4+R5+R6) (R7+R8+R9)*(R10+R1+R12) Rt = ----------------------- + ------------------------- R1+R2+R3+R4+R5+R6 R7+R8+R9+R10+R11+R12 54R * 54R 54R * 54R = ----------- + ----------- = 54 ohms 54R + 54R 54R + 54R That is, if I interpret what you mean by "3P in series with 3P" correctly. If I do, then that's equivalent to "6S in parallel with 6S": --+-[R]-[R]-[R]-[R]-[R]-[R]-+-- | | +-[R]-[R]-[R]-[R]-[R]-[R]-+ Or, simply, ---[R]-[R]-[R]--- Which (except for the fact that you're dealing with 12 resistors instead of 10) is one of the states illustrated in Ed's and my example. -- JF |
Series, parallel, and series-parallel resistors - series parallel R.pdf
"John Fields" wrote in message ... On Sat, 22 Oct 2011 18:33:18 -0700, "Artemus" wrote: Maybe I'm missing what you and Ed are trying to show but per the OP it seems you both are missing some combinations such as 3P in series with 3P = 12ohms. Art --- I was just trying to show the simplest set of series, parallel, and series-parallel connections available using from one to ten equal-valued resistors. There are, indeed, many more combinations available, one of them being the 3P in series with 3P: --+-[R1]-[R2]-[R3]-+--+-[R7]-[R8]-[R9]---+-- | | | | +-[R4]-[R5]-[R6]-+ +-[R10]-[R11]-[R12]+ but the end-to-end resistance isn't 12 ohms, it's: (R1+R2+R3)*(R4+R5+R6) (R7+R8+R9)*(R10+R1+R12) Rt = ----------------------- + ------------------------- R1+R2+R3+R4+R5+R6 R7+R8+R9+R10+R11+R12 54R * 54R 54R * 54R = ----------- + ----------- = 54 ohms 54R + 54R 54R + 54R That is, if I interpret what you mean by "3P in series with 3P" correctly. If I do, then that's equivalent to "6S in parallel with 6S": --+-[R]-[R]-[R]-[R]-[R]-[R]-+-- | | +-[R]-[R]-[R]-[R]-[R]-[R]-+ Or, simply, ---[R]-[R]-[R]--- Which (except for the fact that you're dealing with 12 resistors instead of 10) is one of the states illustrated in Ed's and my example. -- JF Sorry, I didn't mean to be cryptic with my symbols. 3P = 3 18ohm resistors in parallel = 6 ohms. 2 sets of these in series = 12 ohms. Art |
Series, parallel, and series-parallel resistors - series parallel R.pdf
On Sun, 23 Oct 2011 12:37:56 -0700, "Artemus"
wrote: "John Fields" wrote in message .. . On Sat, 22 Oct 2011 18:33:18 -0700, "Artemus" wrote: Maybe I'm missing what you and Ed are trying to show but per the OP it seems you both are missing some combinations such as 3P in series with 3P = 12ohms. Art --- I was just trying to show the simplest set of series, parallel, and series-parallel connections available using from one to ten equal-valued resistors. There are, indeed, many more combinations available, one of them being the 3P in series with 3P: --+-[R1]-[R2]-[R3]-+--+-[R7]-[R8]-[R9]---+-- | | | | +-[R4]-[R5]-[R6]-+ +-[R10]-[R11]-[R12]+ but the end-to-end resistance isn't 12 ohms, it's: (R1+R2+R3)*(R4+R5+R6) (R7+R8+R9)*(R10+R1+R12) Rt = ----------------------- + ------------------------- R1+R2+R3+R4+R5+R6 R7+R8+R9+R10+R11+R12 54R * 54R 54R * 54R = ----------- + ----------- = 54 ohms 54R + 54R 54R + 54R That is, if I interpret what you mean by "3P in series with 3P" correctly. If I do, then that's equivalent to "6S in parallel with 6S": --+-[R]-[R]-[R]-[R]-[R]-[R]-+-- | | +-[R]-[R]-[R]-[R]-[R]-[R]-+ Or, simply, ---[R]-[R]-[R]--- Which (except for the fact that you're dealing with 12 resistors instead of 10) is one of the states illustrated in Ed's and my example. -- JF Sorry, I didn't mean to be cryptic with my symbols. 3P = 3 18ohm resistors in parallel = 6 ohms. 2 sets of these in series = 12 ohms. Art --- Ah, I get it now. ;) |-0.67R-| | | +-[R]-[R]-+ | | +-[R]-[R]-+ | | +-[R]-[R]-+ -- JF |
Series, parallel, and series-parallel resistors - series parallelR.pdf
Artemus wrote:
"ehsjr" wrote in message ... John Fields wrote: A nice PDF. I like it - much better than the text output my program produces (shown below). I programmed it, using the 18 ohm resistors mentioned in the original post. Total R is shown in the right hand column. I like it better your way, with the schematic and the generic R. It works works for any value of R; my program does too, but the output is limited to only one resistor value per run. Your multiplication factor works for any resistance. Here's the output I got: 10 in parallel = 1.8 9 in parallel = 2 8 in parallel = 2.25 7 in parallel = 2.57142857 6 in parallel = 3 5 in parallel = 3.6 4 in parallel = 4.5 3 in parallel = 6 2 in parallel = 9 1 single resistor = 18 1 in series with 9 in parallel = 20 1 in series with 8 in parallel = 20.25 1 in series with 7 in parallel = 20.5714286 1 in series with 6 in parallel = 21 1 in series with 5 in parallel = 21.6 1 in series with 4 in parallel = 22.5 1 in series with 3 in parallel = 24 1 in series with 2 in parallel = 27 1 in series with 1 in parallel = 36 2 in series with 8 in parallel = 38.25 2 in series with 7 in parallel = 38.5714286 2 in series with 6 in parallel = 39 2 in series with 5 in parallel = 39.6 2 in series with 4 in parallel = 40.5 2 in series with 3 in parallel = 42 2 in series with 2 in parallel = 45 2 in series with 1 in parallel = 54 3 in series with 7 in parallel = 56.5714286 3 in series with 6 in parallel = 57 3 in series with 5 in parallel = 57.6 3 in series with 4 in parallel = 58.5 3 in series with 3 in parallel = 60 3 in series with 2 in parallel = 63 3 in series with 1 in parallel = 72 4 in series with 6 in parallel = 75 4 in series with 5 in parallel = 75.6 4 in series with 4 in parallel = 76.5 4 in series with 3 in parallel = 78 4 in series with 2 in parallel = 81 4 in series with 1 in parallel = 90 5 in series with 5 in parallel = 93.6 5 in series with 4 in parallel = 94.5 5 in series with 3 in parallel = 96 5 in series with 2 in parallel = 99 5 in series with 1 in parallel = 108 6 in series with 4 in parallel = 112.5 6 in series with 3 in parallel = 114 6 in series with 2 in parallel = 117 6 in series with 1 in parallel = 126 7 in series with 3 in parallel = 132 7 in series with 2 in parallel = 135 7 in series with 1 in parallel = 144 8 in series with 2 in parallel = 153 8 in series with 1 in parallel = 162 9 in series with 1 in parallel = 180 Ed Maybe I'm missing what you and Ed are trying to show but per the OP it seems you both are missing some combinations such as 3P in series with 3P = 12ohms. Art It's not meant to show all possible combinations. It's meant to show the simple ones in the form shown on John's pdf. I.E. one single set of parallel resistors in series with one single set of series resistors, or those that are purely parallel or purely series. I thought the configurations I had in mind were obvious in the original thread, but apparently they weren't. What's glaring here is in my ugly text output. It shows Rs + Rp, where Rs is the equivalent resistance of the specified number of resistors in series, and Rp is the equivalent resistance of the specified number of resistors in parallel. However, the set of parallel resistors was allowed to consist of a single resistor in my program. One resistor does not make a parallel set! For example, it says "9 in series with 1 in parallel". I needed to change the it to show the resistors in series where it said "with 1 in parallel". The new output appears below. Ed 10 in parallel = 1.8 9 in parallel = 2 8 in parallel = 2.25 7 in parallel = 2.57142857 6 in parallel = 3 5 in parallel = 3.6 4 in parallel = 4.5 3 in parallel = 6 2 in parallel = 9 1 single resistor = 18 1 in series with 9 in parallel = 20 1 in series with 8 in parallel = 20.25 1 in series with 7 in parallel = 20.5714286 1 in series with 6 in parallel = 21 1 in series with 5 in parallel = 21.6 1 in series with 4 in parallel = 22.5 1 in series with 3 in parallel = 24 1 in series with 2 in parallel = 27 2 in series = 36 2 in series with 8 in parallel = 38.25 2 in series with 7 in parallel = 38.5714286 2 in series with 6 in parallel = 39 2 in series with 5 in parallel = 39.6 2 in series with 4 in parallel = 40.5 2 in series with 3 in parallel = 42 2 in series with 2 in parallel = 45 3 in series = 54 3 in series with 7 in parallel = 56.5714286 3 in series with 6 in parallel = 57 3 in series with 5 in parallel = 57.6 3 in series with 4 in parallel = 58.5 3 in series with 3 in parallel = 60 3 in series with 2 in parallel = 63 4 in series = 72 4 in series with 6 in parallel = 75 4 in series with 5 in parallel = 75.6 4 in series with 4 in parallel = 76.5 4 in series with 3 in parallel = 78 4 in series with 2 in parallel = 81 5 in series = 90 5 in series with 5 in parallel = 93.6 5 in series with 4 in parallel = 94.5 5 in series with 3 in parallel = 96 5 in series with 2 in parallel = 99 6 in series = 108 6 in series with 4 in parallel = 112.5 6 in series with 3 in parallel = 114 6 in series with 2 in parallel = 117 7 in series = 126 7 in series with 3 in parallel = 132 7 in series with 2 in parallel = 135 8 in series = 144 8 in series with 2 in parallel = 153 9 in series = 162 10 in series = 180 |
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