What will be the self-inductance of a coil to be connected in a series with a resistance of π √3 Ω such that the phase difference between the e.m.f. and the current at 50 Hz frequency is 30° ?

Question

What will be the self-inductance of a coil to be connected in a series with a resistance of π √3 Ω such that the phase difference between the e.m.f. and the current at 50 Hz frequency is 30° ? (A) 0.5 H (B) 0.03 H (C) 0.05 H (D) 0.01 H

Tardigrade Admin · Accepted Answer

tan φ=(XL/R)=(2 π v L/R) ⇒ tan 30°=(2 π × 50 × L/π √3) ⇒ L=0.01 H

Q. What will be the self-inductance of a coil to be connected in a series with a resistance of $π 3 Ω$ such that the phase difference between the e.m.f. and the current at $50 Hz$ frequency is $3 0^{\circ}$ ?

0.5 H

0.03 H

0.05 H

0.01 H

$tan ϕ = \frac{X _{L}}{R} = \frac{2 π vL}{R}$
$\Rightarrow tan 3 0^{\circ} = \frac{2 π \times 50 \times L}{π 3}$
$\Rightarrow L = 0.01 H$

Q. What will be the self-inductance of a coil to be connected in a series with a resistance of π3​Ω such that the phase difference between the e.m.f. and the current at 50Hz frequency is 30∘ ?