MHT CET · Physics · Alternating Current
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
- A \(44\)
- B \(82\)
- C \(146\)
- D \(242\)
Answer & Solution
Correct Answer
(D) \(242\)
Step-by-step Solution
Detailed explanation
When current is in phase with voltage, we have
\(
\begin{aligned}
& \mathrm{Z}=\mathrm{R}=20 \Omega \\
& \mathrm{e}_0=\sqrt{2} \mathrm{e}_{\mathrm{rms}}=220 \sqrt{2} \mathrm{~V} \\
& \mathrm{i}_0=\frac{\mathrm{e}_0}{\mathrm{Z}}=\frac{220 \sqrt{2}}{20}=11 \sqrt{2} \mathrm{~A} \\
& \mathrm{i}_0=\sqrt{242} \mathrm{~A}
\end{aligned}
\)
\(
\begin{aligned}
& \mathrm{Z}=\mathrm{R}=20 \Omega \\
& \mathrm{e}_0=\sqrt{2} \mathrm{e}_{\mathrm{rms}}=220 \sqrt{2} \mathrm{~V} \\
& \mathrm{i}_0=\frac{\mathrm{e}_0}{\mathrm{Z}}=\frac{220 \sqrt{2}}{20}=11 \sqrt{2} \mathrm{~A} \\
& \mathrm{i}_0=\sqrt{242} \mathrm{~A}
\end{aligned}
\)
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