The capacity of a parallel plate condenser is $10\,\mu F$ without dielectric. Dielectric of constant $2$ is used to fill half the distance between the plates, the new capacitance in $\mu F$ is
Medium
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(d) $C = \frac{{A{\varepsilon _0}}}{d} = 10\,\mu F$
${C_1} = \frac{{A{\varepsilon _0}}}{{d - t + \frac{t}{k}}} = \frac{{A{\varepsilon _0}}}{{d - \frac{d}{2} + \frac{d}{{2k}}}} = \frac{{A{\varepsilon _0}}}{{\frac{d}{2}\left( {1 + \frac{1}{2}} \right)}} = \frac{4}{3}.\frac{{A{\varepsilon _0}}}{d}$
${C_1} = \frac{4}{3} \times 10 = 13.33\,\mu F$
${C_1} = \frac{{A{\varepsilon _0}}}{{d - t + \frac{t}{k}}} = \frac{{A{\varepsilon _0}}}{{d - \frac{d}{2} + \frac{d}{{2k}}}} = \frac{{A{\varepsilon _0}}}{{\frac{d}{2}\left( {1 + \frac{1}{2}} \right)}} = \frac{4}{3}.\frac{{A{\varepsilon _0}}}{d}$
${C_1} = \frac{4}{3} \times 10 = 13.33\,\mu F$
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