# A series LCR circuit driven by

Question:

A series LCR circuit driven by $300 \mathrm{~V}$ at a frequency of $50 \mathrm{~Hz}$ contains a resistance $\mathrm{R}=3 \mathrm{k} \Omega$, 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 $\left.\pi^{2}=10\right)$

1. $4 \mu \mathrm{F}$

2. $25 \mu \mathrm{F}$

3. $400 \mu \mathrm{F}$

4. $40 \mu \mathrm{F}$

Correct Option: 1

Solution:

For maximum average power

$\mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{C}}$

$250 \pi=\frac{1}{2 \pi(50) \mathrm{C}}$

$\mathrm{C}=4 \times 10^{-6}$

Option (1)