An inductor of $0.5 \mathrm{mH}$, a capacitor of $20 \mu \mathrm{F}$ and a resistance of $20 \Omega$ are…
An inductor of $0.5 \mathrm{mH}$, a capacitor of $20 \mu \mathrm{F}$ and a resistance of $20 \Omega$ are connected in series with a $220 \mathrm{~V}$ a.c. source. If the current is in phase with the e.m.f. the maximum current in the circuit is $\sqrt{x} A$. The value of ' $x$ ' is
$44$
$82$
$146$
$242$
Solution
When current is in phase with voltage, we have
$\begin{aligned}
& \mathrm{Z}=\mathrm{R}=20 \Omega \\
& \mathrm{e}_0=\sqrt{2} \mathrm{e}_{\mathrm{rms}}=220 \sqrt{2} \mathrm{~V} \\
& \mathrm{i}_0=\frac{\mathrm{e}_0}{\mathrm{Z}}=\frac{220 \sqrt{2}}{20}=11 \sqrt{2} \mathrm{~A} \\
& \mathrm{i}_0=\sqrt{242} \mathrm{~A}
\end{aligned}$