Question

A coil has an inductance of $0.7 \,H$ and is joined in series with a resistance of $220\, \Omega$. When an AC e.m.f. of $220 \,V , \,50 \,Hz$ is applied to it, find the wattless component of current in the circuit is

• A. 0.2 A
• B. 0.4 A
• C. 0.5 A
• D. 0.7 A

Answer 1

Answer: (C)

$X_{L}=\omega L=2 \pi f L=220\, \Omega$
$\phi=\tan ^{-1}\left(\frac{X_{L}}{R}\right)=\tan ^{-1} \frac{220}{220}=45^{\circ}$
$I=\frac{E}{\sqrt{R^{2}+X_{L}^{2}}}$
$=\frac{220}{\sqrt{(220)^{2}+(220)^{2}}}=\frac{1}{\sqrt{2}}$
Wattless component of current $=I \sin \phi$
$=\frac{1}{\sqrt{2}} \cdot \sin 45^{\circ}=0.5\,A$