**Energy Stored In A Charged Capacitor-**

- The process of charging a capacitor is equivalent to that of transferring charge from one plate to the other plate of the capacitor.
- At any stage of the charging, there exists a potential difference between the plates of the capacitor.
- Therefore, some work must be done to transfer charge from one plate to the other plate of the capacitor.
- This work is stored as
**electrostatic potential energy**in the capacitor.

**Deriving Formula For Energy Stored In Charged Capacitor-**

**Let at any instant, a charge q be on the capacitor. Then, potential difference between the plates of the capacitor is given by-**

**If extra charge dq is transferred to the capacitor, then work done to do so is given by-**

**If the final charge on the capacitor is Q, then the total work done is given by-**

**This work is stored as the electrostatic potential energy (U) of the capacitor. So, we have-**

**(Equation-01)**

**Other Expressions-**

**The above formula for energy stored in a charged capacitor can be expressed in the following two forms-**

**Substituting Q = CV in equation-01, we get-**

**Substituting C = Q/V in equation-01, we get-**

**Thus, energy stored in a charged capacitor is given by the formulae-**

**It is important to note that the electrostatic potential energy of a capacitor is stored in the form of electric field between the plates of the capacitor.**

**Electrostatic Energy Density-**

Energy stored per unit volume of the space between the plates of the capacitor is called as energy density. |

**Consider a parallel plate capacitor having-**

- Electrical capacitance = C
- Area of each plate = A
- Distance between the plates = d

**When the capacitor is charged to voltage V, the energy stored in the capacitor is given by-**

**(Equation-01)**

**But capacitance of a parallel plate capacitor is given by-**

**(Equation-02)**

**If E is the electric field between the plates, then potential difference V across the plates is given by-**

**(Equation-03)**

**Using Equations-02 and 03 in Equation-01, we get-**

**Since volume of the capacitor = Ad. Thus,**

**The SI unit of energy density is J m**^{-3}.**The dimensional formula of energy density is [ML**^{-1}T^{-2}].

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