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  4. A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R =3 k Ω, an inductor of inductive reactance XL=250 π Ω and an unknown capacitor. The value of capacitance to maximize the average power should be: (. Take .π2=10)

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Q. A series LCR circuit driven by $300\, V$ at a frequency of $50\, Hz$ contains a resistance $R =3 k \,\Omega$, an inductor of inductive reactance $X_{L}=250 \pi \,\Omega$ and an unknown capacitor. The value of capacitance to maximize the average power should be: $\left(\right.$ Take $\left.\pi^{2}=10\right)$

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Solution:

For maximum average power
$X_{L}=X_{C} $
$250 \pi=\frac{1}{2 \pi(50) C} $
$C=4 \times 10^{-6}$