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MHT CET · Physics · Alternating Current

An ideal inductor of \(\left(\frac{1}{\pi}\right) \mathrm{H}\) is connected in series with a \(300 \Omega\) resistor.
If a \(20 \mathrm{~V}, 200 \mathrm{~Hz}\) alternating source is connected across the combination, the phase difference between the voltage and current is

  1. A \(\tan ^{-1}\left(\frac{3}{4}\right)\)
  2. B \(\tan ^{-1}\left(\frac{4}{3}\right)\)
  3. C \(\tan ^{-1}\left(\frac{5}{4}\right)\)
  4. D \(\tan ^{-1}\left(\frac{4}{5}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\tan ^{-1}\left(\frac{4}{3}\right)\)

Step-by-step Solution

Detailed explanation

\( X_L = 2 \pi f L = 2 \pi (200 \, \mathrm{Hz}) \left( \frac{1}{\pi} \, \mathrm{H} \right) = 400 \, \Omega \) \( \tan \phi = \frac{X_L}{R} = \frac{400 \, \Omega}{300 \, \Omega} = \frac{4}{3} \)