Solve DC Circuit Problem: Find Potential Difference & Current

[thaer_dude]

Homework Statement

Find
a) the potential difference between points a and b
b) the current of the 20 ohm resistor

I drew the diagram in MS Paint. Should be good enough.

http://img188.imageshack.us/img188/6515/circuitf.jpg

2. The attempt at a solution

I just don't know where to start, since I'm not sure how the current will behave. Will it leave the battery, hit the "intersection" near b, and then split off in all 3 directions? Or will it simply go one way towards b then loop around and go back up to a then take the top wire through the 10 ohm resistor and back in the battery? I don't know, and I'm not sure how I'm supposed to find out.

 

[tramar]

Between points a and b you have 3 resistors. Normally you could simplify them by adding resistances but with that power source there you can't do that. However you can still add the 10 and 5 ohm resistances together and treat them as one path... then the problem reduces to a circuit with two loops. Knowing this you should be able to find all the currents as well as the potential drop on the simplified path.

 

[thaer_dude]

Thanks, that definitely helped, but why can't the "simplified path" and the bottom path with the 20 and 5 ohm resistors be treated as if they were in parallel and then simplified further into one path?

 

[Integral]

Thanks, that definitely helped, but why can't the "simplified path" and the bottom path with the 20 and 5 ohm resistors be treated as if they were in parallel and then simplified further into one path?

Good question! There IS no reason the 5 and 20 Ohm resistors couldn't be treated as a parallel path.