On Fri, 21 Oct 2011 08:54:15 -0500, John Fields
wrote:

--
JF

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

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

"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

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

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

"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

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

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