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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
9×104Hz
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B
16×107Hz
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C
8×105Hz
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D
9×103Hz
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Solution

The correct option is B $$8\times 10^5 Hz$$
For the given case we have standard formula for resonant frequency as:
$$f\:=\dfrac{1}{2\pi}\:\sqrt{\dfrac{1}{LC}-\dfrac{R^2}{L^2}}$$ 
$$f\:=\dfrac{1}{2\pi}\:\sqrt{\dfrac{1}{0.16\times 10^{-3}\times 250\times 10^{-6}}-\dfrac{400}{({0.16\times10^{-3}})^{2}}}$$ 
On directly putting the given values in he equation we get:
$$\omega\:=\:7.98\times10^5$$

Physics

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