Q. The self-inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of
A) 4 $\mu F$
B) 8$\ \mu F$
C) 1$\ \mu F$
D) 2$\ \mu F$
Explanation
(c) Given, $L = 10H,\ f = 50\ Hz$
For maximum power
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ X_{C} = X_{L}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{\omega C} = \ \omega L$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ C = \frac{1}{\omega^{2}L}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ C = \frac{1}{4\pi^{2} \times 50 \times 50 \times 10}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ C = 0.1 \times 10^{- 5}F = 1\ \mu F$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.