Question

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

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

Answer 1

The correct option is C $1\mu \text{F}$

Given:
$L=10\text{H},f=50\text{Hz}$

For maximum power, $X_C=X_L$

or we can say that, $\frac{1}{\omega C}=\omega L$

Substituting the data given in the question gives,

$C=\frac{1}{4{\pi }^2\times 50\times 50\times 10}=0.1\times {10}^{-5}\text{F}\text{or}1\mu F$

Hence, option (c) is the correct answer.