AP Physics: Circuits Mindteaser

[soccerjayl]

Which of the three circuits below contains resistors that are neither in series nor parallel and why?

http://jon8rfc.homeip.net/uploader/uploaded/phys.gif


Currently in AP Physics, so I know have a lead on the question. The first one would be my first guess, because I'm not sure how resistors in diagonal apply to how they are in series or parallel. But then again, NONE of the resistors can be in parallel or series and i think others in the circuit a may be. I also have a feeling it could be B or C, b just because I'm not sure what the middle wiring adds to the circuit and c because i don't think any of them are in series or parallel to each other.

Please help if you can. Thanks.

 

[xanthym]

Which of the three circuits below contains resistors that are neither in series nor parallel and why?

http://jon8rfc.homeip.net/uploader/uploaded/phys.gif


Currently in AP Physics, so I know have a lead on the question. The first one would be my first guess, because I'm not sure how resistors in diagonal apply to how they are in series or parallel. But then again, NONE of the resistors can be in parallel or series and i think others in the circuit a may be. I also have a feeling it could be B or C, b just because I'm not sure what the middle wiring adds to the circuit and c because i don't think any of them are in series or parallel to each other.

Please help if you can. Thanks.

First, let's define "Series" and "Parallel":
1) 2 Resistors are in Series if the CURRENT through both of them is EQUAL.
2) 2 Resistors are in Parallel if the VOLTAGE across both of them is EQUAL.

A ---> In Drawing A (for arbitrary resistance values), the 3 diagonal resistors have NEITHER the same voltage across them NOR the same current through them.
B ---> In Drawing B (for arbitrary resistance values), each vertical pair of resistors has the same voltage across them, and the total current through each successive pair is the same. Further, the current through the lower left single resistor is equal to the total current through all the other resistors. Thus, this circuit can be modeled with 3 pairs of parallel resistors in series with themselves and in series with another single resistor (lower left).
C ---> In Drawing C (for arbitrary resistance values), the top 2 resistors have NEITHER the same voltage across them NOR the same current through them.


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[Davorak]

I think you are incorrect about circuit a. circuit a can be reduce to one resistance. The three diagonal ones are not in are not in series or parallel but the they are in series and or parallel to other resistors.

The top resistor is in series with the top left resistor, combine to make R1. R1 is parallel top diagonal, combine to make R2. R2 is in series with the top right resistor, combine to make R3. R3 is parallel to the middle horizontal resistor, combine to make R4. R4 is in series with the bottom left, combine to make R5. R5 is parallel to the bottom diagonal resistor, combine to make R6. R6 is in series with the bottom left resistor.

So the answer would be c. It is called a Wheatstone bridge. Search on google for Wheatstone bridge.
http://www.google.com/search?hl=en&q=Wheatstone+bridge