Question

A dielectric slab with thickness \[t=\frac{3d}{4}\] and dielectric constant \[K\] is inserted into a gap of separation \[d\). What is the new capacitance in terms of the original capacitance \[C_0\]?

Options

• \[C=\frac{K+3}{4}C_0\]

• \[C=\frac{4}{K+3}C_0\]

• \[C=\frac{4K}{K+3}C_0\]

• \[C=\frac{K+3}{4K}C_0\]

Answer 1

Substituting \[t=3d/4\] into the partial-slab expression gives \[C=4K\varepsilon_0A/[d(K+3)]\]. Since \[C_0=\varepsilon_0A/d\], the ratio is \[C/C_0=4K/(K+3)\].