Question

There is a 5 $\Omega$ resistance in an ac circuit. Inductance of $0.1H$ is connected with it in series. If equation of ac e.m.f. is $5\sin 50t$ then the phase difference between current and e.m.f. is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{4}$
• D. $Zero$

Answer 1

The correct option is C $\frac{\pi }{4}$

Given,

$R=5\Omega L=0.1HE=5sin50t$

Here, $\omega =50$

$X_L=\omega L=50\times 0.1=5\Omega$

$sin\theta =\frac{X_L}{Z}$

$Z=\sqrt{5^2+5^2}=5\sqrt{2}\Omega$

$sin\theta =\frac{5}{5\sqrt{2}}$

$sin\theta =\frac{1}{\sqrt{2}}=sin\frac{\pi }{4}\theta =\frac{\pi }{4}$

Correct option is C