An inductor coil when connected to a 6 V battery draws a steady current of 12 A. This coil is connected to a capacitor and an ac source of voltage 6 V in series. If the current in the circuit is in phase with the emf, the rms current would be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12 A
With a steady (dc) current the inductor has no reactance, so the battery measurement gives only the resistance of the coil.
\( \displaystyle R = \frac{V}{I} = \frac{6\,\mathrm{V}}{12\,\mathrm{A}} = 0.5\,\Omega \)
In the series LCR circuit the current is in phase with the emf only at resonance, where \( X_L = X_C \) and the impedance reduces to R. Taking the 6 V of the ac source as its rms value:
\( \displaystyle Z = \sqrt{R^{2} + (X_L - X_C)^{2}} = R = 0.5\,\Omega \)
\( \displaystyle I_{\mathrm{rms}} = \frac{V_{\mathrm{rms}}}{Z} = \frac{6\,\mathrm{V}}{0.5\,\Omega} \)
\( \displaystyle I_{\mathrm{rms}} = 12\,\mathrm{A} \)