c
(c) Potential difference between the plates \(V = V_{air} + V_{medium}\)
\( = \frac{\sigma }{{{\varepsilon _0}}} \times (d - t) + \frac{\sigma }{{K{\varepsilon _0}}} \times t\)
\(==>\) \(V = \frac{\sigma }{{{\varepsilon _0}}}(d - t + \frac{t}{K})\)
\( = \frac{Q}{{A{\varepsilon _0}}}(d - t + \frac{t}{K})\)
Hence capacitance \(C = \frac{Q}{V} = \frac{Q}{{\frac{Q}{{A{\varepsilon _0}}}(d - t + \frac{t}{K})}}\)
\( = \frac{{{\varepsilon _0}A}}{{(d - t + \frac{t}{k})}} = \frac{{{\varepsilon _0}A}}{{d - t\,\left( {1 - \frac{1}{k}} \right)}}\)