Question

A capacitor and a resistor are connected in series to an ac source of variable frequency. When the frequency of the ac source becomes $ \frac{1}{3} $rd of its initial value, the current in the circuit decreases by 50%. The power factor of the circuit at the initial frequency is

• A. \( \frac{\sqrt{1}}{8} \)
• B. \( \frac{\sqrt{3}}{8} \)
• C. \( \frac{\sqrt{5}}{8} \)
• D. \( \frac{\sqrt{7}}{8} \)

Hint:

In ac circuits with a resistor and capacitor, the power factor depends on the frequency of the ac source.

Answer 1

The Correct Option is C

The power factor of the circuit in an ac circuit is given by the formula: \[ \text{Power Factor} = \cos \phi \] where \( \phi \) is the phase difference between the voltage and the current. Since the current decreases by 50% when the frequency is reduced to \( \frac{1}{3} \)rd of its initial value, the power factor at the initial frequency can be calculated to be \( \frac{\sqrt{5}}{8} \).