Definition of Capacitance:

C = Q/V (1)

Charge = current * time: Q = I*t Solving for voltage:

C*V = I*t (1a)V = I*t/C (2)

Dynamic Voltage:

dV/dt = I/C (3)

Stored Energy:

dV/dt = I/C (3)

At initial voltage Vo At final voltage Vf

Eo = ½ C*Vo2
Ef = ½ C*V2

Delivered energy = Eo - Ef