A series LCR circuit is connected to an ac source of $220 V, 50 Hz$ . The circuit contain a resistance $R = 100 Ω$ and an inductor of inductive reactance $X_{L} = 79.6 Ω$ . The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _________ $μF$ .

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answer is 40.

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Detailed Solution

$\begin{array}{l} X_{L} = X_{c} = \frac{1}{ω C} \\ C = \frac{1}{79.6 \times 2 π \times 50} F \\ = \frac{10^{6}}{79.6 \times 100 π} μF = 39.99 μF ≃ 40 μF \end{array}$

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