Question

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

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

Answer 1

The correct option is D $1\mu F$

Maximum power ($I^{2}R)$ is obtained when $I$ is maximum ( $Z$ is minimum).

For $Z$ minimum, $X_L=X_C$, which yields
$C=\frac{1}{(2\pi n{)}^{2}L}=\frac{1}{4{\pi }^2\times 50\times 50\times 10}$

$\therefore C=0.1\times {10}^{-5}F=1\mu F$