Question

A series LCR circuit contains inductance $5mH$, capacitance $2\mu F$ and resistance 10 $\Omega$. If a frequency A.C. source is varied, what is the frequency at which maximum power is dissipated?

• A. $\frac{{10}^5}{\pi }Hz$
• B. $\frac{{10}^{-5}}{\pi }Hz$
• C. $\frac{2}{\pi }\times {10}^{5}Hz$
• D. $\frac{5}{\pi }\times {10}^{3}Hz$

Answer 1

Answer: (D)

$\frac{5}{\pi }\times {10}^{3}Hz$

Given : $L=5mH=5\times {10}^{-3}H$ $C=2\times {10}^{-6}F$

Maximum power is dissipated at resonant frequency.

Resonant frequency $w_r=\frac{1}{2\pi \sqrt{LC}}$

$\therefore$ $w_r=\frac{1}{2\pi \sqrt{(5\times {10}^{-3})(2\times {10}^{-10})}}$

$⟹$ $w_r=\frac{{10}^4}{2\pi }=\frac{5}{\pi }\times {10}^3$ $Hz$