The capacitance of the Parallel-Plate Capacitor with Dielectric Slab in parallel

As the parallel plate capacitor.

A parallel plate capacitor is an arrangement of two metal plates connected in parallel separated from each other by some distance $d$.

A dielectric medium occupies the gap between the plates.

The dielectric medium can be air, vacuum or some other non conducting material like mica, glass, paper wool, electrolytic gel, and many others.

A dielectric medium occupies the gap between the plates.

Let's study the parallel plate capacitor with dielectric slab in parallel.

Consider, we have a capacitor and it has three slabs of the dielectric.

So the dielectric constants of slabs 1, 2, and 3 are $K_{1}$, $K_{2}$, and $K_{3}$ respectively.

Let the distance between two parallel plates is $d$. Hence the width of all slabs is also $d$.

If the width of these slabs is the same. However, the cross-section area of each slab is different.

Suppose the cross-section area of 1, 2, and 3 slab is $A_{1}$, $A_{2}$, and $A_{3}$ respectively.

The construction of this capacitance is such that the potential difference across each and every slab is the same.

Since the potential difference of these slabs is the same so we can consider as three capacitors are connected in parallel.

The formula of the capacitance of a capacitor is given as.

Then the equivalent capacitance of these slabs is $C$. Where $C_{1}$ is the capacitance of slab 1, $C_{2}$ is the capacitance of slab 2 and $C_{3}$ is the capacitance of slab 3.

So the capacitance $C_{1}$ of slab 1 is.

Similarly, for the capacitance $C_{2}$ of a slab 2 is.

Also, the capacitance $C_{3}$ of the slab 3 is

Now the net effective capacitance $C$ is.

If we have $n$ number of slabs then the general formula for the effective capacitance is.

Revision

The formula of the parallel plate capacitor is given as.

The arrangement of the capacitors with the dielectric slab in parallel is.

This is the expression for solving the capacitors with the dielectric slabs in parallel.