Circuit with Multiple Batteries?

Question

Please help me solve for the magnitude and direction of the current through each resistor (ignore the colons):
_v2___v1__
|::::::::::|:::::::::::|
|:::::::::r2:::::::::|
|_r1__|__r3_|

Thanks in advance! I will give my best answer to the person who can best explain the correct answer and how to get there, not the fastest person.

I can handle the algebra easily, so don't worry about spoon feeding the algebra. I just would like help with the equation part of it.

Thanks in advance!

D'oh! Forgive me for forgetting to add polarities. Both batteries are arranged so that the negative terminal is on the left, and the positive on the right.

Double D'oh! I forgot to post the values:
v1 = 6, v2 = 12, R1 = 10, R2 = 25 and R3 = 30.

My apoligies to those who took the time to try to help me thus far anyway, I'd appreciate it if you'd try one last time with (I hope) all of the needed information now.

Answer 1

Use the current node between r1, r2 and r3. Since the total current is 0 the equation becomes I1 + I2 + I3 = 0 where I1 is the current through r1, etc.

Also use the voltage around the 2 loops as

V2 = I2 * r2 + I1 * r1

and

V1 = I2 * r2 + I3 * r3

I am sure that I have the signs wrong somewhere, but you get the idea.

Now you have 3 equations and 3 unknowns, I1, I2 and I3. Good luck.

Answer 2

First the governing equations are
V1= I1(r2+r3) -I2r2
V2= - I1 r2 + I2(r1+r2)

To determine the magnitude and direction of each current the actual values of voltage souses and resistors are needed.
Substitute these values and solve for the unknown currents I1 and I2.