Devices called capacitors are used to store energy and electric charge. They are frequently found in electronic devices such as flash cameras, laptops, and cell phones. However, how do capacitors actually store energy? We will discuss here.
What is a Capacitor?
Two conducting plates positioned close to one another but without touching make form a capacitor. An insulating substance known as a dielectric such as air, paper, or plastic stands between these plates.
Energy Stored in a Capacitor
A capacitor accumulates a positive charge on one plate and an equivalent amount of negative charge on the other when it is connected to a battery. An electric field is produced between the plates in this configuration.
How Does a Capacitor Store Energy?
Electrons are moved from one plate to the other by the battery when a capacitor is being charged. The electric field between the plates is used to store electrical energy during this process. Until it is released, this energy stays in the capacitor.
Consider inflating a balloon with air. More air (and energy) is stored the more you blow. In a similar vein, energy is stored in a capacitor during charging. It saves more energy the more charge it contains.
Derivation of Energy Stored in a Capacitor
Let’s derive the formula to calculate the energy stored in a capacitor.
Suppose a small amount of charge dq is added to a capacitor which already has a charge q.
The voltage at this moment is V = q/C, where C is the capacitance.
The work done to add this small charge is:
dW = V × dq = (q/C) × dq
To find the total work done, we integrate from 0 to final charge Q:
W = Q / 0 q / C dq = 1 / C Q / 0 q dq = 1 / C⋅ q2 / 2 Q / 0 = Q2 / 2C
This work is stored as energy (U) in the capacitor. So,
U = Q2 / 2C
We can also express energy in terms of voltage or capacitance:
Using Q = CV
U = 1 / 2CV2
Or, using V = Q / C
U = 1 / 2 QV
So, the three common formulas for energy stored in a capacitor are:
U = 1 / 2CV2 = 1 / 2 QV = Q2 / 2C
You can use any of these depending on what quantities are known in a problem.
Where is This Energy Stored?
The capacitor’s electric field between its plates stores energy instead of the plates themselves. Similar to how energy is held in a compressed spring, the energy is found in the electric field that is produced when charges separate.
Energy Density
The energy stored per unit volume in the electric field is called energy density. If E is the electric field and ε₀ is the permittivity of free space, then:
Energy density = Total energy within plates / Volume within plates
Energy Density = 1 / 2ε0E2
This formula helps when studying capacitors with different dielectrics or geometries.
Practical Applications
Because of their capacity to store energy, capacitors are frequently utilised in electronics.
Capacitors in camera flashes store energy and swiftly release it to produce a brilliant flash.
They even out variations in voltage in power supplies.
Capacitors are utilised for energy storage and regenerative braking in electric vehicles, and they store and release energy in defibrillators to aid in heart restarts.
Key Points
Capacitors store electric energy in the electric field between their plates.
This energy is given by:
U = 1 / 2CV2 = 1 / 2QV = Q2 / 2C
Capacitors are useful in circuits that require brief power bursts because they can swiftly release the stored energy, which is derived from the effort the battery does to charge the capacitor.
Van de Graaff Generator:
A Van de Graaff Generator is a device used for building up high potential differences pf the order of a few millions volts. Such high potential differences are used to accelerate charged particles.
A Van de Graaff Generator consists of a large spherical conducting shell (a few meter in diameter). By means of moving belt and suitable brushes. Charge is continuously transferred to the shell and potential difference of the order of several million volts is built up, which can be used for accelerating charged particles.
Conclusion
We can better grasp a capacitor’s function in both basic and sophisticated electronic systems when we understand how energy is stored in it.
This idea is crucial whether you’re trying to construct your own circuit or studying for a test. Although they may appear to be little parts, capacitors are extremely useful instruments in contemporary technology because of their capacity to store and release energy.
The energy (U) stored in a capacitor is given by any of the following formulas:
U = 1 / 2CV2
U = 1 / 2QV
U = Q2 / 2C
Where:
C = capacitance,
V = potential difference (voltage),
Q = charge stored.
Instead of being stored in the capacitor’s actual plates, the energy is stored in the electric field that exists between them. The separation of positive and negative charges produces this electric field.
Work is done to segregate charges onto the plates of a capacitor when it is linked to a power source. Energy is stored in the electric field that is produced by this work. Therefore, the energy is stored in the electric field rather than the actual plates.
Work is done to segregate charges onto the plates of a capacitor when it is linked to a power source. Energy is stored in the electric field that is produced by this work. Therefore, the energy is stored in the electric field rather than the actual plates.
The SI unit of energy is the joule (J). So, energy stored in a capacitor is measured in joules.
Energy density is the energy stored per unit volume in the electric field between the plates. It is given by the formula:
Energy Density = 1 / 2ε0E2
Where:
ε0 = permittivity of free space,
E = electric field between the plates.