Physics - EMI/AC Question with Solution | TestHub

The inductive reactance is $X_L=\omega L=(200\text{rad/s})(2.5\text{H})=500\Omega$. The capacitive reactance is $X_C=\frac{1}{\omega C}=\frac{1}{(200\text{rad/s})(50\times 10^{-6}\text{F})}=\frac{1}{0.01}=100\Omega$. The impedance of the circuit is $Z=\sqrt{R^2+(X_L-X_C{)}^2}=\sqrt{300^2+(500-100{)}^2}=\sqrt{300^2+400^2}=\sqrt{90000+160000}=\sqrt{250000}=500\Omega$. The power factor is $\cos \varphi =\frac{R}{Z}=\frac{300}{500}=0.6$.