Question

A series $LCR$ circuit consists of resistance $R$, inductance $L$ and capacitance $C$. Find power factor of the circuit at frequency which is

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{2}$
• D. 1

Answer 1

Answer: (B)

$\frac{1}{\sqrt{2}}$

Answer 2

The question is incomplete. However, assuming it refers to the half-power frequencies of the LCR circuit, the condition is $|X_L - X_C| = R$. The impedance $Z$ at these frequencies is $Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{R^2 + R^2} = R\sqrt{2}$. The power factor is $\cos \phi = \frac{R}{Z} = \frac{R}{R\sqrt{2}} = \frac{1}{\sqrt{2}}$.