Physics - EMI/AC Question with Solution | TestHub

${\text{V}}_0=\mathrm{10 }V, \omega =314 \mathrm{ rad/s}$

$P=V_{rms}{I}_{rms}\cos \varphi$

$P=V_{rms}\frac{V_{rms}}{Z}\frac{R}{Z}$

$=\frac{{\left(V_{rms}\right)}^{2}R}{Z^2}$

$X_L=\omega L=\left(314\right) \left(20\times {10}^{-3}\right)=6.280$

$X_C=\frac{1}{\omega C}=\frac{1}{314\times 100\times {10}^{-6}}=31.84\mathrm{ \Omega }$

$R=50\mathrm{ \Omega }$

$Z=\sqrt{{\left(X_C-X_L\right)}^2+R^2}$

$= \sqrt{{\left(31.84-6.28\right)}^2+{\left(50\right)}^2}=56\mathrm{ \Omega }$

$\Rightarrow P=\frac{{\left(\frac{10}{\sqrt{2}}\right)}^2\times 50}{{\left(56\right)}^2}=0.79\text{ W}$