Question

As shown in the figure an inductor of inductance $200\, mH$ is connected to an $AC$ source of emf $220 \,V$ and frequency $50 \,Hz$. The instantaneous voltage of the source is $0\, V$ when the peak value of current is $\frac{\sqrt{a}}{\pi} A$. The value of a is ____

Answer 1

$f =50\, Hz$
$X _{ L }=2 \pi fL$
$=2 \pi(50)\left(200 \times 10^{-3}\right)$
$=20\, \pi \Omega$
$i _{0}=\frac{ V _{0}}{ X _{ L }} \Rightarrow \frac{ V _{ rms } \sqrt{2}}{ X _{ L }}$
$=\frac{(220) \sqrt{2}}{20 \pi}=\frac{11 \sqrt{2}}{\pi}$
$i _{ o }=\frac{\sqrt{242}}{\pi}$