d
Average power, \(P=E_{r.m .s} I_{r. m .s} \cos \phi \)

\(Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}, \cos \phi=\frac{R}{Z}\)

But \(I_{\mathrm{r.} \mathrm{m.} \mathrm{s.}}=\frac{E_{\mathrm{r.}, \mathrm{m.s.}}}{Z}, \quad \)

\(\therefore P=E_{\mathrm{r.} \mathrm{m.s.}}^{2} \cdot \frac{R}{Z^{2}}\)

\(\therefore P=E_{\mathrm{r.m.s}}^{2} \frac{R}{\left\{R^{2}+\left(X_{L}-X_{C}\right)^{2}\right\}}\)

\(=\frac{\varepsilon^{2} R}{\left[R^{2}+\left(L \omega-\frac{1}{C \omega}\right)^{2}\right]}\)