# Energy Stored by a Capacitor

## Energy Stored by a Capacitor Revision

**Energy Stored by a Capacitor**

**Capacitors** are very useful when a quick release of energy is needed. This section looks at how we can calculate the amount of **energy stored** by a **capacitor **or the amount of **energy released** by a **capacitor **when discharging.

**Energy Stored by a Capacitor**

As the **capacitor** charges, it stores electrical energy which can later be released. In the process of charging, **electrons** are moved from the **positive plate** to the **negative plate**.

As the negative plate becomes more charged, the **electrostatic force of repulsion** increases, meaning that the circuit needs to do **work **on the electrons to overcome the **electrostatic force**.

Therefore, the **charge** on the capacitor is directly proportional to the **potential difference** of the power supply.

If we were to plot the Potential Difference against the Charge for a parallel plate capacitor, it would look something like this:

The **energy stored by a capacitor** (electrical potential energy) is equal to the **area** under the potential difference-charge graph. The area of a triangle is \dfrac{1}{2} \times \text{base} \times \text{height}, and therefore we can write the **energy stored by the capacitor** as:

E = 0.5QV

We can substitute in the capcitance equation, \left(Q=CV\right):

E = 0.5 CV^2

Both these equations can be used to calculate the **energy stored by a capacitor**.

**Example: **A capacitor of capacitance 2 \: \mu \text{C} requires a potential difference of 75 \: \text{kV} to fully charge. How much electrical potential energy does it store when fully charged?

**[2 marks]**

E = 0.5 CV^2

E = 0.5 \times 2 \times 10^{-6} \times 75000^2

E = 5625 \: \text{J}

## Energy Stored by a Capacitor Example Questions

**Question 1: **Explain the process of how a capacitor charges.

**[2 marks]**

In the process of charging, **electrons are moved from the positive plate to the negative plate.** As **the negative plate becomes more charged, the electrostatic force of repulsion increases, meaning that the circuit needs to do work on the electrons to overcome the electrostatic force.**

**Question 2:** A capacitor of capacitance 1.2 \: \mu \text{F} requires a potential difference of 50 \: \text{kV} to fully charge. How much electrical potential energy does it store when fully charged?

**[2 marks]**

**Question 3:** The charge on a capacitor is 3 \: \mu \text{C} when the potential difference is 150 \: \text{kV}. Calculate the electric potential energy of the capacitor.

**[2 marks]**

## You May Also Like...

### MME Learning Portal

Online exams, practice questions and revision videos for every GCSE level 9-1 topic! No fees, no trial period, just totally free access to the UK’s best GCSE maths revision platform.