The self-inductance of the motor of an electr | vedclass

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(B) For maximum power in an $AC$ circuit, the circuit must be in resonance.At resonance, the inductive reactance equals the capacitive reactance, i.e.

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(B) For maximum power in an $AC$ circuit, the circuit must be in resonance.At resonance, the inductive reactance equals the capacitive reactance, i.e., $X_L = X_C$.The resonant frequency is given by $f = \frac{1}{2 \pi \sqrt{LC}}$.Squaring both sides, we get $f^2 = \frac{1}{4 \pi^2 LC}$.Rearranging for capacitance $C$, we get $C = \frac{1}{4 \pi^2 f^2 L}$.Given $L = 10\;H$ and $f = 50\;Hz$.Substituting the values: $C = \frac{1}{4 	imes \pi^2 	imes (50)^2 	imes 10}$.Using $\pi^2 \approx 10$, we get $C = \frac{1}{4 	imes 10 	imes 2500 	imes 10} = \frac{1}{1000000} = 10^{-6}\;F$.Thus, $C = 1\;\mu F$.

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 (in $\mu F$) of:

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