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Well, In this article, we are going to derive the expression for capacitance of parallel plate capacitor when a dielectric slab of thickness t is inserted between the plates. Wants to know all about the derivation, stay tuned with us till end…

# DERIVATION FOR THE CAPACITANCE

Let’s take a **parallel plate capacitor** having plates surface area is **A**. A dielectric slab of thickness t is inserted between the plates. And the dielectric slab have the **dielectric constant** K and the permittivity of it’s medium is ε. See figure below :

After putting **dielectric** slab of thickness t the remaining distance will be (d – t). Let the electric field inside the dielectric slab is E and field inside the plates and outside the slab is .

## DERIVATION PROCESS

The **electric field** inside the slab is given as-

And the **electric field** outside the slab is given as –

The total **potential difference** between the plates is given as the sum of the **potential difference** due to the slab and due to without slab. Which is clearly written below :

**Capacitance of any capacitor is given as charge per unit potential difference**. Let’s put the value of potential difference in the formula of capacitance.

This is the required value of capacitance of parallel plate capacitor when a dielectric slab of thickness t is inserted between the plates.

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