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Question:

In an AC circuit voltage V = V0 sin ωt and inductor L is connected across the circuit. Then the instantaneous power will be?

V202wl sin wt

−V202wl sin wt

V20wl sin wt

V202wl sin 2wt

Solution:

Instantaneous power is given by: P = V(t)i(t)
For the given circuit, −L(di/dt) = V0sinωt ⇒ i = −(V0/L)∫sinωtdt = (V0/ωL)cosωt.
Thus, instantaneous power, P = (V0²/2ωL)sin2ωt