a
Impedance \(Z\) in an \(ac\) circuit is

\(Z=\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}} ;\) where \(X_{C}=\) capacitive reactance and \(X_{L}=\) inductive reactance.

Also \(X_{C}=\frac{1}{\omega C}\) and \(X_{L}=\omega L\)

\(\therefore \quad z=\sqrt{(50)^{2}+\left(\frac{1}{314 \times 100 \times 10^{-6}}-314 \times 20 \times 10^{-3}\right)^{2}}\)

or \(\quad Z=56\, \Omega\)

The power loss in the circuit is \(P_{a v}=\left(\frac{V_{r m s}}{Z}\right)^{2} R\)

\(\therefore \quad P_{a v}=\left(\frac{10}{(\sqrt{2}) 56}\right)^{2} \times 50=0.79\, \mathrm{W}\)