Capacitance

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Question

The capacitance of a parallel plate capacitor with air as medium is $6 μF$ With the introduction of a dielectric medium, the capacitance becomes $30 μF$ The permittivity of the medium is $(ε_{0} = 8 .55 \times 10^{- 12} C^{2} N^{- 1} m^{- 2})$

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Solution

$C_{air} = \frac{ε_{0} A}{d}$
$\begin{array}{l} C_{med} = \frac{{Kε}_{0} A}{d} \\ C_{med} = {KC}_{air} \\ 30 = K 6 \\ K = 5 \\ \frac{ε}{ε_{0}} = 5 \end{array}$
$\begin{array}{l} ε = 5 ε_{0} = 5 \times 8 .85 \times 10^{- 22} \\ = 0 .44 \times 10^{- 10} \end{array}$

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