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  4. 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:

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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:

AIEEEAIEEE 2005Alternating Current

Solution:

Given: $L =10\, H, f= 50\, Hz$
For maximum power
$X_C=X_L$
$\frac{1}{\omega C}=\omega L$
$C=\frac{1}{\omega^{2}L}$
$\therefore C=\frac{1}{4\,\pi^{2}\times50\times50\times10}$
$C=0.1\times10^{-5}\,F=1\,\mu F$