Question

An inductor has a resistance $R$ and inductance $L$. It is connected to an AC source of emf $E_v$ 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

The correct option is C $\frac{E_v}{\sqrt{R^2+{\omega }^2{L}^2}}$

The impedance in R-L circuit is

$Z=\sqrt{R^2+X_L^2}=\sqrt{R^2+(\omega L{)}^2}$

The current, $I_v=\frac{E_v}{Z}$
$=\frac{E_v}{\sqrt{R^2+(\omega L{)}^2}}$