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. 0

Answer 1

Answer: (C)

$\frac{\pi}{4}$

Answer 2

$\cos\varphi = \frac{R}{Z} = \frac{R}{\sqrt{R^{2} + \omega^{2}L^{2}}} = \frac{5}{\sqrt{25 + (50)^{2} \times (0.1)^{2}}}$

$= \frac{5}{\sqrt{25 + 25}} = \frac{1}{\sqrt{2}} \Rightarrow \varphi = \pi/4$