# Parallel Plate Capacitor-

Before you go through this article, make sure that you have gone through the previous article on Parallel Plate Capacitor.

We have learnt-

• A parallel plate capacitor is an arrangement of two equally & oppositely charged plates of equal area separated by a certain distance through a dielectric.
• The capacitance of an air filled parallel plate capacitor is given by-

• The capacitance of a parallel plate capacitor completely filled with a dielectric is given by-

• The capacitance of an air filled parallel plate capacitor increases to K times when a dielectric having dielectric constant K is filled between its plates.

## Capacitance of Parallel Plate Capacitor Partially Filled With Dielectric-

Let us consider a parallel plate capacitor having-

• Q = Magnitude of charge on each plate
• A = Area of each plate
• d = distance between its two plates
• a dielectric having dielectric constant K and thickness t (t < d) between its two plates

Now, we wish to find the capacitance of a parallel plate capacitor partially filled with a dielectric.

### Step-01: Calculating the Potential difference Across Capacitor (V)-

We know,

• A uniform electric field exists between the two plates of capacitor.
• If σ is the surface charge density of each plate, then electric field between the two plates (in free space) is given by-

• Then, the electric field inside the dielectric placed in the electric field Eo is given by-

Let VA = Electric potential of plate A and VB = Electric potential of plate B.

To calculate the potential difference across the capacitor, we find the potential difference between its two plates i.e. VA – VB.

We travel from plate A to plate B and write the changes in electric potential. Then, we have-

(Equation-02)

### Step-02: Calculating the Capacitance of Capacitor (C)-

We know, the capacitance of a capacitor is given by the formula-

Substituting equation-02, we get-

Thus, the capacitance of a parallel plate capacitor partially filled with a dielectric is given by the formula-

OR

### Special Case-

If the dielectric is completely filled between the two plates of the capacitor, then t = d.

Substituting t = d in the above formula, we get-

We derived the same formula in the previous article also.