# Simplifying A Parallel Circuit

Discussion in 'Homework Help' started by RoF112, Jun 10, 2012.

1. ### RoF112 Thread Starter New Member

Jun 9, 2012
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I already know the equation for the following parallel circuit:
R1||R2||R3||R4||R5 (all the resistors are in parallel)

but I want some more insight as to how to obtain that answer.
I followed the redrawing method explained in this website, but for some reason, I could not arrive at that particular equation. Any help?

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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One obvious approach is to realize that one end of every resistor can be traced by direct connection back to the positive battery terminal. In the same manner, the opposite end of each resistor can be traced by direct connection back to the negative battery terminal. This automatically leads one to the conclusion that all resistors are in parallel with the battery and hence with each other.

3. ### absf Senior Member

Dec 29, 2010
1,850
505
OK, in fig B, R1 and R2 are in parallel and replaced by R12.
In fig C, R4 and R5 are also in parallel and replaced by R45.
In fig D, R3 is rotated clockwise.
Now does it look more obvious that all the 3 resistors are in parallel?

Allen

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4. ### WBahn Moderator

Mar 31, 2012
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6,884
Either of these work. A slightly more explicit way of applying t_n_k's suggestion is to label the node coming out of the positive end of the battery 'P' and then write 'P' at every place where that same node touches a resistor. Now do the same for the node connected to the negative end of the battery, but use the label 'N'. Now look at each resistor and you will see that it is connected to node 'P' on one side and node 'N' on the other, hence they are in parallel.