3 resistors in parallel: how to get there

[Granger]

Homework Statement

2. Homework Equations [/B]

Hi! So I was given the following circuit with R=15k

I was asked to calculate the equivalent resistance between A and B.

The Attempt at a Solution

[/B]
According to my professor this circuit is equivalent to a circuit with three resistors in parallel, so the resistance is the parallel of the 3 resistances R (= 5k).

However I don't understand how it is equivalent.

My professor explanation was that no matter what pad we choose for a current it will pass only through a resistor (which I totally understand why!). However I don't see how that means mathematically that they are in parallel. Can someone help me clarify it?.

Thanks!

 

[berkeman]

The easiest way for me on this problem is to re-draw the circuit. Start with A at the top and B at the bottom, and label the resistors in the original figure R1, R2, R3 from left-to-right. Then you can see that R1 and R2 are in parallel going from A at the top to B at the bottom. Do you now see where R3 goes?

 

[Granger]

The easiest way for me on this problem is to re-draw the circuit. Start with A at the top and B at the bottom, and label the resistors in the original figure R1, R2, R3 from left-to-right. Then you can see that R1 and R2 are in parallel going from A at the top to B at the bottom. Do you now see where R3 goes?

Starting with A we go through R1 and then the circuit parts into R2 and a short circuit (so R1 and R2 are in parallel). After that we have B and R3 (so R1 and R3 are in parallel). Then after R2, we have the same situation (R2 and R3 in parallel).

So if R1 and R2 are in parallel, R2 and R3 and then R1 and R3 then the 3 resistors are in parallel?

 

[berkeman]

So if R1 and R2 are in parallel, R2 and R3 and then R1 and R3 then the 3 resistors are in parallel?

Yes, but I didn't follow your description, sorry. Start by "pulling" A up to the top of the circuit, which pulls the left of R1 up and the right end of R2 up toward A. Do you see how you can do this because those two ends of R1 and R2 are shorted together by the wire? Then do similar things rotating the rest of the circuit...

 

[Granger]

Yes, but I didn't follow your description, sorry. Start by "pulling" A up to the top of the circuit, which pulls the left of R1 up and the right end of R2 up toward A. Do you see how you can do this because those two ends of R1 and R2 are shorted together by the wire? Then do similar things rotating the rest of the circuit...

Oh I finally got it! Thank you very much !

 

[phinds]

Just FYI, that circuit has appeared here on PF numerous times. It is a standard problem to make sure students really understand series/parallel concepts and that they can redraw a circuit to make things more clear.