Heat Generation in a circuit due to moving charges

[deepak-]

1. Homework Statement
A capacitor of capacitance C id charged by a battery of emf E and inernal resistance r, A resistance 2r is also connected in series with the capacitor. The amount of heat liberated inside the battery by the time capacitor is 50% charged is? Answer is E²/C



2. Homework Equations
q=Q(1-e^-t/RC)
btw, RC means the time constant and Q is the charge at steady state



3. The Attempt at a Solution
tried to find time when charge in capacitor is 50% charged and then find the heat using V²/R but had no success

 

[gneill]

The voltage and current are changing with time as the capacitor charges. This suggests that some calculus will be involved.

Hint: ∫ watts*dt = Energy

 

[gneill]

You might also note that the answer suggested in the problem statement is clearly incorrect, as the units of E²/C are not energy.