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# Energy Stored by a Capacitor

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Capacitors are commonly used to store electrical energy and release it when needed. They store energy in the form of electrical potential energy.

## How do capacitors store energy?

Capacitance is the ability of a capacitor to store charge, which is measured in Farad. Capacitors are usually used in conjunction with other circuit components to produce a filter that allows some electrical impulses to pass while blocking others.

Figure 1. A capacitor. Source: Dwayne Madden, Flickr (CC BY 2.0).

Capacitors are made of two conductive plates and an insulator material in between them. When a capacitor is connected to a circuit, the positive pole of the voltage source begins to push the electrons from the plate to which it is connected. These pushed electrons gather in the other plate of the capacitor, causing excess electrons to be stored in the plate.

Figure 2. Diagram of a charged capacitor. Source: Oğulcan Tezcan, StudySmarter.

The excess electrons in one plate and their corresponding lack in the other cause a potential energy difference (voltage difference) between the plates. Ideally, this potential energy difference (charge) remains unless the capacitor begins to discharge in order to supply voltage back to the circuit.

However, in practice, there are no ideal conditions, and the capacitor will begin to lose its energy once it is taken out of the circuit. This is because of what is known as leakage currents out of the capacitor, which is an unwanted discharging of the capacitor.

### The effect of the dielectric on the stored charge

How long a capacitor can store energy depends on the quality of the dielectric material between the plates. This insulating material is also known as the dielectric. How much energy a capacitor stores (its capacitance) is decided by the surface area of the conductive plates, the distance between them, and the dielectric between them, which is expressed as follows:

Here:

• C is capacitance, measured in Farad.
• is the dielectric constant of the insulator material.
• A is the area of plate overlap (m ^ 2).
• d is the distance between the plates, measured in metres.

The table below indicates how much effect the dielectric material has on the energy stored by the capacitor.

 Material Dielectric constant Air 1.0 Glass (window) 7.6-8 Fibre 5-7.5 Polyethylene 2.3 Bakelite 4.4-5.4

## How to calculate the energy stored in a capacitor

Since the energy stored in a capacitor is electrical potential energy, it is related to the charge (Q) and the voltage (V) of the capacitor. First, let’s remember the equation for electrical potential energy (ΔPE), which is:

This equation is used for the potential energy (ΔPE) of a charge (q) while going through a voltage difference (ΔV). When the first charge is placed in the capacitor, it goes through a change of ΔV=0 because the capacitor has zero voltage when it is not charged.

When the capacitor is fully charged, the final charge being stored in the capacitor experiences a voltage change of ΔV=V. The average voltage on a capacitor during the charging process is V/2, which is also the average voltage experienced by the final charge.

Here:

• is the energy stored in a capacitor, measured in Joules.
• Q is the charge on a capacitor, measured in Coulombs.
• V is the voltage on the capacitor, measured in Volts.

We can express this equation in different ways. The charge on a capacitor is found from the equation Q = C*V, where C is the capacitance of the capacitor in Farads. If we put this into the last equation, we get:

Now, let’s consider some examples.

A heart defibrillator is giving out 6.00 ⋅ 10^2 J of energy by discharging a capacitor, which initially is at 1.00 ⋅ 10 ^ 3 V. Determine the capacitance of the capacitor.

The energy of the capacitor (Ecap) and its voltage (V) are known. As we need to determine the capacitance, we need to use the relevant equation:

Solving for the capacitance (C), we get:

Adding the known variables, we then have:

The capacitance of a capacitor is known to be 2.5 mF, while its charge is 5 Coulombs. Determine the energy stored in the capacitor.

As the charge (Q) and the capacitance (C) are given, we apply the following equation:

Adding the known variables, we get:

## Energy Stored by a Capacitor - Key takeaways

• Capacitance is the storing ability of a capacitor, which is measured in Farad.
• How long a capacitor can store energy is determined by the quality of the insulator material (dielectric) between the plates.
• How much energy a capacitor stores (its capacitance) is determined by the surface area of the conductive plates, the distance between them, and the dielectric between them.
• The equation used to determine the capacitance is C = (ε0 ⋅ A) / d.
• The equation used to determine the energy stored in the capacitor is E = (Q ⋅ V) / 2.

We can determine the energy stored by a capacitor with the equation E = (Q * V) / 2.

Electrical potential energy.

How long a capacitor can store energy is determined by the quality of the insulator material between the plates.

The energy stored in an ideal capacitor remains in between the plates of the capacitor once it is disconnected from the circuit.

Storage cells store energy in the form of chemical energy. When they are connected to a circuit, this energy transforms into electrical energy and is then used.

## Final Energy Stored by a Capacitor Quiz

Question

A 20 mF capacitor has 10 V voltage. How much energy is stored in the capacitor?

1 J.

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Question

A 30 mF capacitor has a charge of 0.2 Coulombs. How much energy is stored in the capacitor?

0.67 J.

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Question

The energy stored in a capacitor is 20 J, and the voltage on the capacitor is 20 V. What is the capacitance of the capacitor?

0.1 F.

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Question

A capacitor has a charge of 10 coulombs and a voltage of 5 V. What is the energy stored by the capacitor?

25 J.

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Question

The energy stored in a capacitor is 15 J, and the capacitor has a charge of 5 Coulombs. What is the capacitance of the capacitor?

0.83 F.

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Question

What is the unit of capacitance?

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Question

Which equation is used to calculate the charge of a capacitor?

Q = C * V.

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Question

If the voltage change on a capacitor is given as V, what is the average voltage on the capacitor during the charging process?

V/2.

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Question

What is the symbol of a capacitor’s charge?

Q.

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Question

How long a capacitor can store energy is determined by the quality of the insulator material between the plates. True or false?

True.

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Question

How much energy a capacitor stores (i.e., its capacitance) is determined by the surface area of the conductive plates, the distance between them, and the dielectric between them. True or false?

True.

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Question

Does the dielectric constant of the dielectric material affect the capacitance of the capacitor?

Yes, it does.

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Question

What is the name given to the insulator material between the plates of a capacitor?

Dielectric.

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Question

What is the name given to the storing ability of a capacitor?

Capacitance.

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Question

In practice, a capacitor begins to lose its energy once it is taken out of the circuit. Why does this happen?

Because of leakage currents.

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