Capacitance of the Parallel Plate Capacitor with Dielectric Slab

Capacitor is used in the circuit of camera of our mobile phones.

When we press the button to take the picture, then a charge is released to the capacitor.

Once the charge released reaches the peak level, the capacitor discharges causing a flash.

If we need a buildup energy and then a sudden release, then we use the capacitor. Hence capacitor is used for the energy storage.

Here, we are going to find the capacitance of a parallel plate capacitor with a dielectric slab.

Letâ€™s find the capacitance.

Consider we have two parallel plate capacitors, one is positively charged and another is negatively charged.

Now we are introducing a dielectric slab in between the parallel plates of capacitor.

Let the thickness of the slab is $t$ and the distance between parallel plates of capacitor is $d$.

In dielectric slab the negative charges are deposited at the side of the positive plate of capacitor and the positive charge at the side of negative plate.

The opposite charges deposition on the dielectric is the process of polarization.

Due to polarization, the charge density $Ïƒ$ is like,

Now there is the electric field $E_{p}$ present in the dielectric slab in the direction as shown,

It is also having the external electric field $E_{0}$ between the parallel plate capacitor in the opposite direction of $E_{p}$.

So the net electric field $E$ inside the slab is.

If there is no dielectric slab then the electric field $E_{0}$ is,

And the capacitance of parallel plate when there is no dielectric slab is,

When we are adding the dielectric slab, then the net potential $V$ of the capacitor is,

As the dielectric constant $K$ is given as,

Now, putting the value of $E$ in the formula of potential of the capacitor, we get,

Here, we put the value of the $E_{0}$ then we get the ratio of $Q$ and $V$ as,

The ratio of the $Q$ by $V$ is the capacitance, $C$. So the capacitance of the parallel plate capacitor is,

If the thickness $t$ of the slab is equal to the distance$d$ between the parallel plates, then the capacitance $C$ is,

This equation indicates that the capacitance of the parallel plate capacitor has got increased by a factor of $K$.

Revision

This is the arrangement of the parallel plate capacitor with a dielectric slab.

This is the formula of the capacitance of the parallel plate capacitor with dielectric slab.

If the dielectric slab thickness is equal to the distance between the parallel plates, then capacitance increases by a factor of $K$.