Question

An inductor has a resistance R and Inductance L. It is connected to an A.C. source of $e.m.f \, E_{v}$, and angular frequency- $\omega$, then the current $I_v$ in the circuit is

• A. $\frac{E_v}{\omega L}$
• B. $\frac{E_v}{R}$
• C. $\frac{E_v}{\sqrt{R^2+\omega^2 L^2}}$
• D. $\sqrt{\left(\frac{E_v}{R}\right)^2+\left(\frac{E_v}{\omega L}\right)^2}$

Answer 1

Answer: (C)

The impedance in R-L circuit is
$Z =\sqrt{ R ^{2}+ X _{ L }^{2}}=\sqrt{ R ^{2}+(\omega L )^{2}}$
The current, $I _{ v }=\frac{ E _{ V }}{ Z }$
$=\frac{ E _{ V }}{\sqrt{ R ^{2}+(\omega L )^{2}}}$