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

Question

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 .

TestHub · Accepted Answer

The average rate at which energy supplied i.e. power delivered is maximum in case of the resonance, therefore

$X_{C} = X_{L}$

$\Rightarrow \frac{1}{ω C} = 79.6 Ω$

$\Rightarrow C = \frac{1}{ω \times 79.6} = \frac{1}{2 π f \times 79.6} = \frac{1}{100 π \times 79.6} = 40 μF$

Hence, $C = 40 μF$ .

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