An inductor coil joined to a 6 V battery draws a steady current of 12 A. This coil is connected to a capacitor and an A C source of rms voltage 6 V in series. If the current in the circuit is in phase with the emf, find the rms current.

The resistance of the coil is $\mathrm{R}=\frac{{\mathrm{V}}_{\mathrm{DC}}}{{\mathrm{I}}_{\mathrm{DC}}}=\frac{6}{12}=0.5 \mathrm{\Omega }$.

In the AC circuit, the current is in phase with the emf. This means that the net reactance of the circuit is zero. 

Hence, the impedance of the circuit is equal to the resistance, i.e., $\mathrm{Z}=\mathrm{R}=0.5 \mathrm{\Omega }$.

$\therefore {\mathrm{I}}_{\mathrm{rms}}=\frac{{\mathrm{V}}_{\mathrm{rms}}}{\mathrm{Z}} =\frac{6}{0.5}=12 \mathrm{A}$.