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  • A capacitor discharges through an inductor of 0.1 henry. If the frequency of discharge is 1000 Hz, calculate the capacitance.Option: 1 <img alt="\mat

A capacitor discharges through an inductor of 0.1 henry. If the frequency of discharge is 1000 Hz, calculate the capacitance.

Option: 1

\mathrm{0.25\mu F }


Option: 2

\mathrm{0.50\mu F }


Option: 3

\mathrm{0.90\mu F }


Option: 4

\mathrm{0.75\mu F }


Answers (1)

best_answer

The frequency of discharge in the L.C circuit is given by

{\begin{aligned} &\mathrm f=\frac{1}{2 \pi \sqrt{\mathrm L C}} \\ & \Rightarrow \mathrm {L C}=\frac{1}{4 \pi^2 \mathrm f^2} \quad \Rightarrow \mathrm C=\frac{1}{4 { \pi^2 \mathrm L \mathrm f^2}} \end{aligned}}

Putting the values of L and f we obtain,

\begin{aligned}\mathrm{ C} & =\frac{1}{4 \times(3.14)^2 \times 1 \times 10^{-1} \times(1000)^2} \cdot \mathrm{F} .=\frac{10}{4 \times(3.14)^2} \mu \mathrm{F} \\\\ & =0.25 \mu \mathrm{F} \end{aligned}

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Riya

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