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)

We know that
(Resonating frequency is given by)
$f_0=\frac{1}{2\pi \sqrt{LC}}$
$f_0=\frac{1}{2\pi \sqrt{5\times 10^{-3}\times 2\times 10^{-6}}}$
where $L=5\times 10^{-3}H$
$C=2\times 10^{-6}F$
$=\frac{1}{2\pi \sqrt{10^{-8}}}=\frac{1}{2\pi \times 10^{-4}}$
$=\frac{10^4}{2\pi }Hz=\frac{5\times 10^3}{\pi }Hz$