# Circuit with 3 batteries and 4 resistors

1. Oct 21, 2014

### icesalmon

1. The problem statement, all variables and given/known data
The question pertains to the first problem from this link
https://courses.physics.illinois.edu/phys212/sp2014/practice/practice.pl?exam2/fa10
They ask for the value of "I" in terms of V1, V2, R1, and R2.
2. Relevant equations
V = IR
∑Vi = 0

3. The attempt at a solution

Choosing Kirchoff's Voltage Law will produce three equations....

1). V1 - i1R1 - V2 - i2R1 - i1R2 = 0

2). V2 - V2 - i3R1 + i2R1 = 0

3). V1 - i1R1 - V2 - i3R1 - i1R2 = 0

The question makes it seem as if I could solve for that current with just one equation. i'm confused on how to label the currents given the positioning of the battery terminals in the circuit as well. They seem to be pumping current directly into each others positive terminals, why is this an efficient set up for the circuit in the first place? Should I combine the two V2 batteries because voltages in parallel are equal?

2. Oct 21, 2014

### icesalmon

okay so just messing with these equations, I3 = I2 and (1) and (3) become the same exact thing, working with just one equation
V1 - i1R1 - V2 - i2R1 - i1R2 = 0

3. Oct 21, 2014

### Staff: Mentor

Check the current sum at one of the nodes. The sum of incoming currents is equal to the sum of outgoing currents.

4. Oct 22, 2014

### icesalmon

I'm sorry, I completely forgot my node equation. I found it quite easily after that third equation. Thank you

5. Oct 22, 2014

### CWatters

Exam questions don't have to be representative of real world problems but you do come across circuits where one voltage source delivers current to another like this. I bet you have at least one battery charger at home. If you have one that charges several loose cells it's not to dissimilar.