Q. The self inductance of the motor of an electric fan is $10H$. In order to impart maximum power at $50\ Hz$, it should be connected to a capacitance of
A) 1 $\mu F$
B) 2 $mF$
C) 4 $mF$
D) 8 $mF$
Explanation
(a) For imparting max power
$X_{L} = X_{C} \Rightarrow \omega L = \frac{1}{\omega C}$
$C = \frac{1}{\omega^{2}L} = \frac{1}{(2\pi f)^{2} \times L} = \frac{1}{(100\pi)^{2} \times 10} = 1 \times 10^{- 6} = 1\mu F$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.