A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance and an inductor of inductive reactance . The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _______

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Solution

Q.
A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains 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 _________ $μF$ . [2023]

Ans.
(40)

To maximize the average rate at which energy is supplied, i.e. power will be maximum.

So in LCR circuit power will be maximum at the condition of resonance and in resonance condition

$X_{L} = X_{C}$

$79.6 = \frac{1}{ω C}$

$∴$ $C = \frac{1}{2 π \times 50 \times 79.6} = 40 μ F$

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