Question

A condenser of $250\, \mu F$ is connected in parallel to a coil of inductance $0.16 \,mH$, while its effective resistance is $20 \,\Omega$. Determine the resonant frequency.

• A. $ 9\times 10^4 \,Hz$
• B. $ 16\times 10^7 \,Hz$
• C. $ 8\times 10^5 \,Hz$
• D. $ 9\times 10^3 \,Hz$

Answer 1

Answer: (C)

The resonant frequency is given by
$f_{0}=\frac{1}{2 \pi} \sqrt{\frac{1}{L C}-\frac{R^{2}}{L^{2}}},$
where $ R=$ resistance and
$L=$ inductance.
$\Rightarrow f_{0}=\frac{1}{2 \pi} \sqrt{\frac{1}{L C}-\frac{R^{2}}{L^{2}}}$
$=\frac{1}{2 \times 3.14} \sqrt{\frac{1}{250 \times 10^{-6} \times 0.16 \times 10^{-3}}-\frac{20 \times 20}{\left(0.16 \times 10^{-3}\right)^{2}}}$
$=8 \times 10^{5} Hz$