Question

A voltage v = v₀ sin ωt applied to a circuit drives a current i = i₀ sin (ωt + Φ) in the circuit. The average power consumed in the circuit over a cycle is ______.

Options

• Zero

• i₀ v₀ cos Φ

• `(i_0 v_0)/2`

• `(i_0 v_0)/2` cos Φ

Answer 1

A voltage v = v₀ sin ωt applied to a circuit drives a current i = i₀ sin (ωt + Φ) in the circuit. The average power consumed in the circuit over a cycle is `bbunderline((i_0 v_0)/2 cos phi)`.

Explanation:

Given: v = v₀ sin ωt

i = i₀ sin (ωt + Φ)

Average power over a full cycle is:

P_av = v_rmsi_rmscos Φ

= `v_0/sqrt 2 i_0/sqrt 2 cos phi`

= `(v_0 i_0)/2 cos phi`