# Energy Stored in a Capacitor

The use of capacitors is very common in various devices like handheld electronic calculators, railway fans, etc. But how is energy stored in a capacitor? In this context, you will get to know how a capacitor holds energy, along with the calculation of the same.

What is a Capacitor?

The capacitor is an electrical energy storing device. Additionally, most capacitors contain two terminals located side by side while an insulator is present between them. In some cases, this whole unit is modified into a compact device in order to save space. Moreover, there are few capacitors which have multiple layers in them for additional functionalities.

How Does a Capacitor Hold Energy?

Two positive charges cannot do anything with one another. Instead, they move away from each other as quickly as they can. However, if the two charges are made to come closer forcibly, they resist. Also, it requires energy to make them come close.

Furthermore, the energy needed does not stray or get utilised. Rather, it gets stored in the form of an electric field which is a type of tension; provided the charges are clasped together, uncomfortably.

Moreover, when the charges again have the liberty to move, they utilise energy to speed them up. Thus, it can be said that capacitors are those components that store electric fields.

Evaluation of Energy Stored in a Capacitor

Let us consider a capacitor is charged to a certain amount of voltage V, and its energy is needed to be calculated. So, energy (or work) W required to move a positive charge close to another one is the product of the positive charge Q and voltage (potential difference).

δW    =     Q        x     δV

(joules)=(coulombs)x(volts)

However, as per common logic, some individuals may feel that a capacitor with charge V needs energy of QV joules to reach the desired state, and hence the capacitor is holding QV joules of energy. However, that is not the case.

Instead, as the charges move nearer and nearer to each other, their resisting property keeps on increasing till it becomes fierce. It is a non-linear procedure. Hence, the only process for energy stored in a capacitor derivation is using the method of integration.

For example, assume that capacitor C is storing a charge Q. So, measuring the voltage V across it can be done quite easily. Further, after applying a small amount of energy, a bit of charge can be induced to the system. Therefore, in terms of Q, an expression can be written.

δW = V δQ = $\frac{Q}{C}$ δQ

After understanding this equation, by integration of the complete δW, requiring energy to push charge Q to the capacitor can also be evaluated.

W=$\frac{1}{C}$$\int_{0}^{Q}$QdQ = $\frac{1}{C}$ $\frac{Q²}{2}$= $\frac{1}{2}QV$

Take a look at the below expression for energy stored in capacitor.

W = $\frac{1}{2}$CV² (joules)

Moreover, here is a solved numerical which will make you understand the calculation better.

Numerical

(i) A capacitor has a capacitance of 50F and it has a charge of 100V. Find the energy that this capacitor holds.

Solution. According to the capacitor energy formula:

U = 1/ 2 (CV2)

So, after putting the values:

U = ½ x 50 x (100)2 = 250 x 103 J

Do It Yourself

1. The Amount of Work Done in a Capacitor which is in a Charging State is:

(a) QV (b) ½ QV (c) 2QV (d) QV2

By going through this content, you must have understood how capacitor stores energy. Additionally, for more knowledge about capacitors, circuits, and other concepts of Physics, download our Vedantu app. Along with easy access to study materials; it also offers online interactive sessions for better understanding of these topics.

1. What is the Derivation of an Expression for Energy Stored in a Capacitor?

Ans. According to the energy stored in a capacitor formula:

dW = dQ × V = Q × dQ​/ C

After integration:

U = 0​∫UdW

= 0Q (Q × dQ ) / C

= Q2 / 2 C

=​ 1 / 2 (CV2)

2. How much Electricity can a Capacitor Store?

Ans. 1-farad capacitor at a voltage of 1 volt stores 1-coulomb charge. Moreover, 1 coulomb is equivalent to 6.25e18 (6.25 x 1018) electrons, and a current of 1 amp shows an electron flow rate of one coulomb each second. Hence a capacitor of 1 farad at 1 volt can store one ampere-second electron.

3. A Charged Capacitor Stores Energy in what Form?

Ans. The energy form in a charged capacitor is electric potential energy, and hence associated with voltage V and charge Q on the capacitor.