Energy balance of the capacitor

Stored energy

The energy stored in a capacitor charged to a voltage uc is: Ec = (1/2)Cuc^2

This energy is zero when uc = 0 and is at its maximum, equal to (1/2) * C * E², when the capacitor is fully charged to voltage E.

Energy balance during charging

During a full charge (from 0 to infinity), the total energy supplied by the generator is W_gen = EQ_final = E(CE) = CE² (the generator supplies a charge Q = C*E at a constant voltage E).

However, the energy stored in the capacitor is only (1/2)CE^2. The difference, which is also (1/2)CE^2, is dissipated as Joule heat in the resistor R, regardless of the value of R!

Summary during discharge

All the energy initially stored, (1/2)CU₀², is entirely dissipated as heat in R during discharge (there is no longer a generator to supply any more).

Summary table

Phase	Energy supplied	Energy stored (final)	Energy dissipated in R
Charging (0 → E)	C*E²	(1/2)CE²	(1/2)CE²
Discharge (U₀ → 0)	0	0	(1/2)CU₀²

Common misconception

A common misconception is to believe that the energy dissipated as Joule heat during charging depends on R. This is incorrect: it is always (1/2)CE^2, regardless of R. However, R does influence the DURATION (via τ = R*C) over which this dissipation takes place, but not its total amount.