Question

A capacitor and a resistor are connected in series to an ac source. If the ratio of the capacitive reactance of the capacitor and the resistance of the resistor is 4:3, then the power factor of the circuit is:

• A. 0.3
• B. 0.8
• C. 0.6
• D. 0.5

Hint:

The power factor is also the cosine of the phase angle between the voltage and current in an AC circuit.

Answer 1

The Correct Option is C

The power factor \( \cos(\phi) \) is given by: \[ \cos(\phi) = \frac{R}{Z} \] where \( Z = \sqrt{R^2 + X_C^2} \). Given \( \frac{X_C}{R} = \frac{4}{3} \), we find: \[ Z = R \sqrt{1 + \left(\frac{4}{3}\right)^2} = R \sqrt{1 + \frac{16}{9}} = R \sqrt{\frac{25}{9}} = \frac{5R}{3} \] Thus, \( \cos(\phi) = \frac{R}{\frac{5R}{3}} = 0.6 \).