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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:

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$4 μ F$

$2 μ F$

$8 μ F$

$1 μ F$

answer is C.

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Detailed Solution

$P = \frac{V^{2}}{Z}$

For max^m power, Z_min = R

So, $X_{L} = X_{C}$

$ω L = \frac{1}{ω C}$

$C = \frac{1}{ω^{2} L} = \frac{1}{4 π^{2} {(50)}^{2} \times 10}$

$C = \frac{1}{1000000}$

$C = 1 μ F$

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