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(A) The total separation between the plates is $d$. The thickness of the dielectric slab is $t = \frac{3d}{4}$.The remaining air gap is $d - t = d - \

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$\frac{4KC_{0}}{3+K}$

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(A) The total separation between the plates is $d$. The thickness of the dielectric slab is $t = \frac{3d}{4}$.The remaining air gap is $d - t = d - \frac{3d}{4} = \frac{d}{4}$.The capacitance $C$ of a parallel plate capacitor with a dielectric slab of thickness $t$ and dielectric constant $K$ is given by the formula:$C = \frac{\epsilon_{0}A}{d - t + \frac{t}{K}}$Substituting the given values $t = \frac{3d}{4}$ and $C_{0} = \frac{\epsilon_{0}A}{d}$:$C = \frac{\epsilon_{0}A}{d - \frac{3d}{4} + \frac{3d}{4K}}$$C = \frac{\epsilon_{0}A}{\frac{d}{4} + \frac{3d}{4K}}$$C = \frac{\epsilon_{0}A}{\frac{d}{4} \left(1 + \frac{3}{K}\right)} = \frac{4\epsilon_{0}A}{d \left(\frac{K+3}{K}\right)}$$C = \frac{4\epsilon_{0}A}{d} \cdot \frac{K}{K+3}$Since $C_{0} = \frac{\epsilon_{0}A}{d}$,we get:$C = \frac{4KC_{0}}{K+3}$

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