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Artemus[_4_] Artemus[_4_] is offline
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Default 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