For the series $L C R$ circuit connected with $220 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c source as shown

Question

For the series $L C R$ circuit connected with $220 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c source as shown in the figure, the power factor is $\frac{\alpha}{10}$. The value of $\alpha$ is $\_\_\_\_$ .

Professor PC Thomas Classes · Answer

The power factor of a series LCR circuit is given by $\cos\phi = \frac{R}{Z}$, where the impedance is $Z = \sqrt{R^2 + (X_L - X_C)^2}$. By evaluating the inductive reactance $X_L = \omega L$ and capacitive reactance $X_C = \frac{1}{\omega C}$ using the parameters given in the circuit diagram, the net impedance $Z$ is calculated. The ratio $\frac{R}{Z}$ evaluates to $0.6$, which can be written as $\frac{6}{10}$. Thus, the value of $\alpha$ is 6.