If in a L-R series circuit the power factor is 1/2 and R=100Ω, then the value of L is, when AC mains is used

Options

(a) πH
(b) √3/π H
(c) π/√3 H
(d) √2/π H

Correct Answer:

√3/π H

Explanation:

power factor, cos ɸ = 1 / 2 ⇒ ɸ = 60°

Therefore, tan 60° = ωL / R ⇒ √3 = (2πv × L) / 100

L = [(√3 × 100) / (2π × 50)] = (√3 / π) H