A sinusoidal voltage v(t) = 100 sin 1000 t is applied a pure capacitor of 100μF. The power is given by

Concept:

Current through a pure capacitor is given by

\(I_{C} = C \frac{dV}{dt}\)

Where;

I_C → Current through capacitor

V→ Applied voltage across the capacitor

And

Power = v(t) × i(t)

Calculation:

Given;

v(t) = 100 sin 1000 t

C = 100 μF

Then;

\(I_{C} = C \frac{dV}{dt} = 100 × 10^{-6} × \frac{d}{dt}(100\sin 1000t )= 10\cos 1000t \)

Therefore;

Power = v(t) × i(t)

            = 100 sin 1000 t × 10 cos 1000t

            = 1000sin(1000t)cos(1000t)

            = 500sin2000t (∵ 2sinθcosθ = sin2θ )