Question

A resistance of 300 Ω and an inductance of $\frac{1}{\pi}$ henry are connected in series to a ac voltage of 20 volts and 200 Hz frequency. The phase angle between the voltage and current is
(a) $tac^{-1} \frac{4}{3}$
(b) $tac^{-1} \frac{3}{4}$
(c) $tac^{-1} \frac{3}{2}$
(d) $tac^{-1} \frac{2}{5}$

Answer 1

answer : option (A) $tan^{-1} \frac{4}{3}$

explanation : resistance , R = 300 Ω

inductance , L = 1/π H

frequency, f = 200 Hz

so, angular frequency, $\omega$ = 2π(200) = 400π rad/s

inductive reactance, $X_L=\omega L$

= 400π × 1/π = 400 H/s = 400Ω

we know, phase angle , $tan\phi=\frac{X_L}{R}$

$tan\phi=\frac{400\Omega}{300\Omega}$

hence, $\phi=tan^{-1}\frac{4}{3}$