A \( 50\,\Omega \) resistance and an inductance of \( \displaystyle\frac{2}{3\pi}\,\mathrm{H} \) are connected in series with power supply of 220 volt AC of 50 Hz. Choose the correct statement:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Potential difference leads the current by \( \tan^{-1}\left(\displaystyle\frac{4}{3}\right) \)
In a series LR circuit the voltage leads the current by a phase angle \( \phi \) with \( \tan\phi = X_L/R \).
\( \displaystyle X_L = 2\pi f L = 2\pi \times 50 \times \frac{2}{3\pi} = \frac{200}{3}\,\Omega \)
\( \displaystyle \tan\phi = \frac{X_L}{R} = \frac{200/3}{50} = \frac{4}{3} \)
\( \displaystyle \phi = \tan^{-1}\left(\frac{4}{3}\right) \)
So the potential difference leads the current by \( \tan^{-1}(4/3) \).