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The rms value of conduction current in a parallel plate capacitor is $6.9 \mu \mathrm{A}$ . The capacity of this capacitor, if it is connected to $230 \mathrm{~V}$ ac supply with an angular frequency of $600 \: \mathrm{rad} / \mathrm{s}$ , will be:

Option: 1
$5 \mathrm{pF}$

Option: 2
$50 \mathrm{pF}$

Option: 3
$100 \mathrm{pF}$

Option: 4
$200 \mathrm{pF}$

Answers (1)

best_answer

$\mathrm{\left(i_c\right)_{r m s} =6.9 \mu \mathrm{A} }$

$\mathrm{ V_{r m s} =230 \mathrm{~V} }$

$\mathrm{ \omega =600\left(\frac{\mathrm{rad}}{\mathrm{s}}\right) }$

$\mathrm{V_{\text {rms }} =I_{r m s}\left(X_c\right)}$

$\mathrm{ 230 =6.9 \times 10^{-6}\left(\frac{1}{600 \times c}\right) }$

$\mathrm{ C =\frac{6.9 \times 10^{-6}}{2.3 \times 6 \times 10^4} }$

$\begin{array}{rl} & =0.5 \times 10^{-10} \\ \end{array}$

$\mathrm{C =50 \times 10^{-12} \mathrm{~F} }$

$\mathrm{C =50 \mathrm{pF} }$

Hence (2) is correct option.

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shivangi.shekhar

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