Question

The self inductance of the motor of an electric fan is $10H$. In order to impart maximum power at $50Hz$, it should be connected to a capacitance of

• A. $4\mu F$
• B. $8\mu F$
• C. $1\mu F$
• D. $2\mu F$

Answer 1

Answer: (C)

$1\mu F$

Given:$L=10$H,$f=50$Hz.

For maximum power, $X_c=X_L$ using resonance condition

or $\frac{1}{\omega C}=\omega L$

or $C=\frac{1}{{\omega }^{2}L}$

$\therefore C=\frac{1}{4{\pi }^2\times 50\times 50\times 10}$

$\therefore C=\frac{49}{4\times 22\times 22\times 2500\times 10}$

$=0.1\times {10}^{-5}$F

$=1\mu$F