Question

The power factor of an L-R series circuit is $0.5$ and that of a C-R series circuit is $0.2$ . If the elements $(L,CandR)$ of the two circuits are joined in series and connected to the same ac source, the power factor of this circuit is found to be $1$ . The ratio of the resistance in the L-R circuit to the resistance in the C-R circuit is

• A. $2$
• B. $\sqrt{2}$
• C. $2\sqrt{2}$
• D. $4$

Answer 1

Answer: (C)

$\frac{R_1}{\sqrt{X_L^2+R_1^2}}=0.5$
${\left(2R_1\right)}^2=R_1^2+X_L^2$
$3R_1^2=X_L^2$ .....(i)
$\frac{R_2}{\sqrt{X_C^2+R_2^2}}=0.2$
$25R_2^2=X_C^2+R_2^2$
$24R_2^2=X_C^2=X_L^2$ (Since the LCR circuit is in resonance, the capacitive reactance and the inductive reactance are equal)
$3R_1^2=24R_2^2$
$\frac{R_1}{R_2}=2\sqrt{2}$