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Question

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

A
$$16\times 10^7$$ Hz
B
$$8\times 10^5$$ Hz
C
$$9\times 10^4$$Hz
D
$$9\times 10^3$$ Hz
Solution
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Correct option is C. $$8\times 10^5$$ Hz
Given
Capacitance, $$C= 250\mu F= 250\times 10^{-6} F$$
Inductance , $$L=0.16mH= 0.16 \times 10^{-3}H$$

Resonant frequency , $$f=\dfrac1{2\pi \sqrt{LC}}= \dfrac1{2\times 3.14\times \sqrt{250\times 10^{-6} \times 0.16 \times 10^{-3}}}= 8\times 10^5 Hz$$

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