An alternating emf \( (\xi) = 220 \sin (50 \pi t) \) is applied to an inductive circuit having self inductance of \( \sqrt{2}\,\pi^{-1}\,\mathrm{H} \). What will be the reading of a.c. ammeter connected in the circuit?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2.2\,\mathrm{A} \)
In a purely inductive circuit the current is limited by the inductive reactance \( X_L = \omega L \), and an a.c. ammeter reads the rms value of the current.
Comparing with \( \xi = \xi_0\sin\omega t \):
\( \xi_0 = 220\,\mathrm{V} \)
\( \omega = 50\pi\,\mathrm{rad\,s^{-1}} \)
\( \displaystyle X_L = \omega L = 50\pi \times \frac{\sqrt{2}}{\pi} = 50\sqrt{2}\,\Omega \)
\( \displaystyle I_0 = \frac{\xi_0}{X_L} = \frac{220}{50\sqrt{2}} = \frac{4.4}{\sqrt{2}}\,\mathrm{A} \)
\( \displaystyle I_{\mathrm{rms}} = \frac{I_0}{\sqrt{2}} = \frac{4.4}{2} = 2.2\,\mathrm{A} \)