Question 92: AC fundamentals

Question

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

Accepted Answer

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
$$
\begin{aligned}
& 	herefore X_{L}=X_{C} \\
& 79.6=\frac{1}{2 \pi(50) 	imes C} \\
& C=\frac{1}{79.6 	imes 2 \pi(50)} \\
& \approx 40 \mu \mathrm{F}
\end{aligned}
$$

AC fundamentals

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