First slide

AC Circuits

Question

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

Moderate

A

$\frac{π}{2}$
B

$\frac{π}{6}$
C

$\frac{π}{4}$
D

0

Solution

$cosφ = \frac{R}{Z} = \frac{R}{\sqrt{R^{2} + ω^{2} L^{2}}} = \frac{5}{\sqrt{25 + {(50)}^{2} \times {(0 .1)}^{2}}}$
$= \frac{5}{\sqrt{25 + 25}} = \frac{1}{\sqrt{2}} \Rightarrow φ = π / 4$

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