**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.

**In this article, we will learn about the parallel plate capacitor partially filled with a dielectric.**

**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 E_{o}is given by-

Let **V _{A} = Electric potential of plate A** and

**V**.

_{B}= Electric potential of plate BTo calculate the potential difference across the capacitor, we find the potential difference between its two plates i.e. V_{A} – V_{B}.

**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.**

**Read the next article on-**

**Series Combination of Capacitors**

**Get more notes & other study material of the Chapter** **Electrostatic Potential & Capacitance**.