An inductor of self inductance 1 H connected in series with a resistor of \(100 \pi \mathrm{ohm}\) and an ac supply of \(100 \pi\) volt, 50 Hz. Maximum current flowing in the circuit is ________ A.

Impedance of circuit
\(\begin{aligned}
& \mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}\right)^2}=\sqrt{\mathrm{R}^2+\left(\omega_{\mathrm{L}}\right)^2} \\
& =\sqrt{(100 \pi)^2+(2 \pi \times 50 \times 1)^2} \\
& =\sqrt{(100 \pi)^2+(100 \pi)^2} \\
& =\sqrt{2} \times 100 \pi \\
& \mathrm{I}_{\mathrm{rms}}=\frac{V}{2}=\frac{100 \pi}{\sqrt{2} \times 100 \pi}=\frac{1}{\sqrt{2}} \\
& \mathrm{I}_{\max }=\sqrt{2} \mathrm{I}_{\mathrm{rms}}=\sqrt{2} \times \frac{1}{\sqrt{2}}=1 \text { Ampere }
\end{aligned}\)
Correct Answer : 1