Capacitors and resistor question?

Short answer: yes, E = 1/2 CV^2 is the total energy dissipated in the resistor.

Basically, you're discharging the capacitor via a resistor. With time, all the energy

stored in the capacitor in the electric field is dissipated via the resistor. The equation

you gave is the total energy stored in the capacitor.

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If you're up to the task, you can prove it!

From P = IV, and E = Pt

or dE = Pdt = IVdt = V²/R dt

This integration is done from t=0 to t = infinity.

Use V = Vp*exp(-t/RC) and

E = ∫{Vp*exp(-t/RC)}²/R dt

to establish that

E = Vp²C/2, Vp is the peak (fully charged) voltage across the

capacitor (resistor as well).

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Hope this helps