Question

The average power dissipated in a pure inductor of inductance L when an ac current is passing through it, is
(a) $\frac{1}{2} LI^2$
(b) $\frac{1}{4} LI^2$
(c) 2 Li²
(d) Zero

Answer 1

Correct Answer :

option d: zero

Explanation :

The average power  dissipated in a circuit consisting only of inductors or capacitors is zero.

power =1/T ∫v(t)i(t)dt

In sinusoidal wave, V and I differ by 90 °

Pa=ω2π∫Aωsin(ωt)cos(ωt)dt

where A is a constant depending on the value of the inductance L or capacitance C of the component.

P=Aω²/2π  [ ∫2π/sin(2ωt)dt]

period of sin(2ωt) is T′=π/ω

interval of integration of P is exactly two periods of sin(2ωt)

so finally :

P=Aω²/2π∫sin(2ωt)dt=0 [ integral from o to 2T']

Answer 2

Answer:

The average power dissipation in pure inductance is 0