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  4. 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 μ F.

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Q. A series LCR circuit is connected to an ac source of $220\, V , 50\, Hz$. The circuit contain a resistance $R =100\, \Omega$ and an inductor of inductive reactance $X _{ L }=79.6\, \Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ________$\mu F$.

JEE MainJEE Main 2023Alternating Current

Solution:

To maximize the average rate at which energy supplied i.e. power will be maximum.
So in LCR circuit power will be maximum at the condition of resonance and in resonance condition
$X_L =X_C$
$79.6 =\frac{1}{\omega C}$
$\therefore C =\frac{1}{2 \pi \times 50 \times 79.6} $
$\therefore C =40 \mu F$