Capacitance of a parallel plate capacitor bec | vedclass

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(D) The capacitance of a parallel plate capacitor with air is given by $C = \frac{\varepsilon_0 A}{d}$.When a dielectric slab of thickness $t$ and die

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$2$

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(D) The capacitance of a parallel plate capacitor with air is given by $C = \frac{\varepsilon_0 A}{d}$.When a dielectric slab of thickness $t$ and dielectric constant $K$ is inserted,the new capacitance $C'$ is given by $C' = \frac{\varepsilon_0 A}{d - t + \frac{t}{K}}$.Given that $C' = \frac{4}{3}C$ and $t = \frac{d}{2}$,we substitute these values:$\frac{\varepsilon_0 A}{d - \frac{d}{2} + \frac{d/2}{K}} = \frac{4}{3} 	imes \frac{\varepsilon_0 A}{d}$.Simplifying the equation:$\frac{1}{\frac{d}{2} + \frac{d}{2K}} = \frac{4}{3d} \Rightarrow \frac{1}{\frac{d}{2}(1 + \frac{1}{K})} = \frac{4}{3d}$.$\frac{2}{d(1 + 1/K)} = \frac{4}{3d} \Rightarrow \frac{2}{1 + 1/K} = \frac{4}{3}$.$6 = 4(1 + 1/K) \Rightarrow 6 = 4 + \frac{4}{K}$.$2 = \frac{4}{K} \Rightarrow K = 2$.

Capacitance of a parallel plate capacitor becomes $4/3$ times its original value if a dielectric slab of thickness $t = d/2$ is inserted between the plates ($d$ is the separation between the plates). The dielectric constant of the slab is

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