Question

A series $LCR$ circuit contains inductance $5\, mH$, 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)

We know that
(Resonating frequency is given by)
$f_{0}=\frac{1}{2 \pi \sqrt{L C}}$
$f_{0}=\frac{1}{2 \pi \sqrt{5 \times 10^{-3} \times 2 \times 10^{-6}}}$
where $L=5 \times 10^{-3} H$
$C=2 \times 10^{-6} F$
$=\frac{1}{2 \pi \sqrt{10^{-8}}}=\frac{1}{2 \pi \times 10^{-4}}$
$=\frac{10^{4}}{2 \pi}\, Hz =\frac{5 \times 10^{3}}{\pi} Hz$