Question

V0 = 10V, $\omega$ = 314 rad/s
P = Vrms irms cos$\varphi$
$$\begin{gathered} =V_{rms}\left(\frac{V_{rms}}{\sout{z}}\right)\left(\frac{R}{\sout{z}}\right)=\frac{{\left(V_{rms}\right)}^{2}R}{{\sout{z}}^2} \\ {X}_L = {\omega }_L = \left(314\right) (20 \times {10}^{–3}) = 6.280 \\ {X}_c=\frac{1}{ {\omega }_c}=\frac{1}{314\times 100\times {10}^{-6}}=31.84\Omega \\ R = 50\Omega \\ \sout{z}=\sqrt{{\left(X_c-X_L\right)}^2+R^2} \\ =\sqrt{{\left(31.84-6.28\right)}^2+}(50{)}^2=50\Omega \\ \Rightarrow P=\frac{{\left({\displaystyle \frac{10}{\Omega }}\right)}^2\times 50}{{\left(56\right)}^2}=0.79W \end{gathered}$$