Q. A coil of inductive reactance $31\Omega$ has a resistance of $8\Omega$. It is placed in series with a condenser of capacitative reactance $25\Omega$. The combination is connected to an a.c. source of $110\ volt$. The power factor of the circuit is
A) 0.80
B) 0.33
C) 0.56
D) 0.64
Explanation
(a) $X_{L} = 31\Omega,\ X_{C} = 25\Omega,\ R = 8\Omega$
Impedance of series $LCR$ is
$Z = \sqrt{(R)^{2} + \left( X_{L} - X_{C} \right)^{2}}$
$= \sqrt{(8)^{2} + (31 - 25)^{2}} = \sqrt{64 + 36} = 10\Omega$
Power factor, $\cos\phi = \frac{R}{Z} = \frac{8}{10} = 0.8$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.