Calculating Energy in an RC Circuit

[Jahosaphatz]

Homework Statement

I have an RC Circuit. There's the EMF (voltage supplier; battery), a resistor, and a capacitor. They are all in series. I need to prove that

--the energy stored in the capacitor through it charging equals 1/2 the energy supplied by the EMF

Then I need to show

--how much energy is lost by the resistor (which should be the other 1/2 of the energy supplied by the EMF by conservation of energy) and I need to prove it other than just using conservation of energy.

Since this problem is all ratios, you can use whatever variables you want (E, i, Q, V, etc) so long as they cancel

Homework Equations

P = dW/dt

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

q = Q(1-e^(-t/(RC)))

There may be more I need.. I really don't know..

The Attempt at a Solution

I'm thinking to use power, which is dW/dt, and integrate indefinitely. I don't know how to incorporate the charging equation, but I'm pretty sure its part of determining the energy of the capacitor?

 

[phyzguy]

You're on the right track. Use I = dQ/dt, calculate the current through the resistor, use this to calculate the power, and integrate.