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MHT CET · Physics · Alternating Current

When a d.c voltage of \(200 \mathrm{~V}\) is applied to a coil of self-inductance \(\left(\frac{2 \sqrt{3}}{\pi}\right) \mathrm{H}\), a current of 1A flows through it. But by replacing d.c. source with a.c. source of \(200 \mathrm{~V}\), the current in the coil is reduced to \(0.5 \mathrm{~A}\). Then the frequency of a.c. supply is

  1. A \(100 \mathrm{~Hz}\)
  2. B \(60 \mathrm{~Hz}\)
  3. C \(75 \mathrm{~Hz}\)
  4. D \(50 \mathrm{~Hz}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(50 \mathrm{~Hz}\)

Step-by-step Solution

Detailed explanation

When a d.c. voltage is applied
\(
\mathrm{R}=\frac{\mathrm{V}}{1}=\frac{200}{1}=200 \Omega
\)
When a.c. voltage is applied
\(
\begin{aligned}
& \mathrm{Z}=\frac{\mathrm{V}}{1}=\frac{200}{0.5}=400 \Omega \\
& \mathrm{Z}^2=\mathrm{R}^2+\mathrm{X}_{\mathrm{L}}^2 \\
& (400)^2=(200)^2+\mathrm{X}_{\mathrm{L}}^2 \\
& \mathrm{X}_{\mathrm{L}}=200 \sqrt{3} \Omega \\
& 2 \pi \mathrm{fL}=2 \pi \mathrm{f} \times \frac{2 \sqrt{3}}{\pi}=200 \sqrt{3} \\
& \mathrm{f}=50 \mathrm{~Hz}
\end{aligned}
\)