How to calculate power provided by a battery

[miaou5]

Homework Statement

The diagram is of a circuit with 2 resistors in series (1 ohm and 2 ohms) connected to 2 batteries (a 9 V battery and a 12 V battery). The question asks, how much energy is provided by the 12-volt battery in 3 seconds?

Homework Equations

Power = IV = I^2R = V^2/R

I = current, V = voltage, R = resistance

The Attempt at a Solution

I used P = I^2R at first, since I already calculated I (= 1 amp) for a previous part. Thus, P = ((1)^2)*(1+2) = 3 watts. It's over 3 seconds, so it would be 3 watts * 3 seconds = 9 joules. However, when I use P = IV, I get a different answer; P = (1)*(12) = 12 watts. 12 watts * 3 sec = 36 joules.

How is this possible? I thought the equations were equivalent--if anyone could shed some light on this, that would be great! Thank you so much.

 

[aralbrec]

How much energy is being supplied by the 9v source?

 

[CWatters]

I already calculated I (= 1 amp) for a previous part.

That suggests the 12V and 9V batteries are arranged to give 3V across the resistors. Correct?

I used P = I^2R at first, since I already calculated I (= 1 amp) for a previous part. Thus, P = ((1)^2)*(1+2) = 3 watts

That's the equation for the power dissipated in the resistors which might be different to that delivered by the 12V battery. aralbrec has given you a good clue as to why these two are not the same thing. What's happening to the 9V battery?