Question

A coil of inductance $L$ and resistance $R$ is connected to an A.C source of $V$ volt. If the angular frequency of the A.C source is equal to $\omega rad{s}^{-1}$, then the current in the circuit will be _____

• A. $\frac{V}{R}$
• B. $\frac{V}{R+L}$
• C. $\frac{V}{L}$
• D. $\frac{V}{\sqrt{R^2+{\omega }^2{L}^2}}$

Answer 1

Answer: (D)

$\frac{V}{\sqrt{R^2+{\omega }^2{L}^2}}$

$\therefore Z=\sqrt{R^2+{\omega }^2{L}^2}I=\frac{V}{Z}\therefore I=\frac{V}{\sqrt{R^2+{\omega }^2{L}^2}}$