How Is Power Calculated in a Circuit with Two Batteries and Resistors?

[tomrja]

Homework Statement

Two batteries with emf e1 = 20.00 V and emf e2 = 19.00 V and no internal resistance are connected to two resistors with resistance R1 = 2.00 ohm and R2 = 8.00 ohm as shown in the figure.

What is the power being delivered by the battery with e1?

Homework Equations

P=IV and P=V^2/R

The Attempt at a Solution

I have done the first two parts of this problem that are not show. Those parts are What is the magnitude of the current through R1? and What is the magnitude of the current through R2? I1=10A and I2=0.125A. I have tried to find the power generated by the battery by finding the change in potential across R1 with the equation V=IR and found that to be 20V. Then, I plugged the 20V into the equation P=IR and used the 10A that I calculated earlier and got an answer of 200W. What am I doing wrong?

 

[Dick]

It looks right to me so far as current. And 200W is consumed by R1. But there is power also being consumed by R2. Use P=IV on the battery in the center. There aren't just 10A going through it. What about the current flowing through the right loop? BTW don't double post, ok? Even if you are in a hurry.

 

[gneill]

I have done the first two parts of this problem that are not show. Those parts are What is the magnitude of the current through R1? and What is the magnitude of the current through R2? I1=10A and I2=0.125A. I have tried to find the power generated by the battery by finding the change in potential across R1 with the equation V=IR and found that to be 20V. Then, I plugged the 20V into the equation P=IR and used the 10A that I calculated earlier and got an answer of 200W. What am I doing wrong?

P=IR is not a valid equation. How could you plug 20V into it, when it doesn't have a voltage term?

What is the total current flowing through ε1? What direction through ε1 is it flowing (from + to - or from - to +)?