Question

A parallel-plate capacitor has the air as a medium between its plates and its capacitance is C. A slab of the dielectric constant K is introduced so as to fill the left half of space of the capacitor, as shown. What is the new capacitance of the capacitor?

Answer 1

When the medium is air, the capacitance, $C=\frac{A{ϵ}_0}{d}$ where A be the area of plates and d be the separation between plates.

When slab is introduced, the whole capacitors will break into two capacitors $C_1$(with slab) and $C_2$ (without slab) and they are in parallel.

Here, $C=\frac{\left(A/2\right)K{ϵ}_0}{d}=KC/2$

and $C_2=\frac{\left(A/2\right){ϵ}_0}{d}=C/2$

Thus, new capacitance is $C_p=C_1+C_2=KC/2+C/2=\frac{C}{2}(K+1)$