An inductor coil joined to a 12 V battery draws a steady current of 12 A. This coil is connected to a capacitor and ac source of rms voltage 12 V in series. What will be the rms current, if the current in the circuit is in phase with the emf?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 12 A
With a steady (dc) current the coil’s inductance plays no part, so the battery reading gives the coil’s resistance.
\( \displaystyle R = \frac{V}{I} = \frac{12\,\mathrm{V}}{12\,\mathrm{A}} = 1\,\Omega \)
In the series LCR circuit, current in phase with the emf means \( X_L = X_C \): the circuit is at resonance, and the impedance reduces to R.
\( Z = \sqrt{R^{2} + (X_L - X_C)^{2}} = R = 1\,\Omega \)
\( \displaystyle I_{\mathrm{rms}} = \frac{V_{\mathrm{rms}}}{Z} = \frac{12\,\mathrm{V}}{1\,\Omega} = 12\,\mathrm{A} \)