# Capacitor and Capacitance: How does capacitor work and store energy

The most widely used electronic component is the Capacitor. The capacitor is a passive circuit element but it doesn’t absorb electric energy rather it store it. The main purpose of the capacitor is to store electric energy for a very short duration of time. The capacitor is also known as a condenser. Capacitors are the application of static electricity.

## Capacitor construction:

A capacitor contains two metallic plates (conducting plates) distant by a dielectric (non-conducting material or insulator). There are different types of capacitors available in the market, all of them have the same fundamental principle.

Practically, the conducting plate may be aluminum sheet and non-conducting material may be air, ceramic, paper, mica etc. A capacitor can be plugged into the circuit as presented in the diagram. Where voltage $V$ provide charge (electrons) to the plate connected to the negative terminal and the same source take charge (electrons) from the plate connected to the positive terminal. The total charge $q$ stored upon the conducting plates is directly proportional to the supply voltage.

$q\quad \propto\quad v$
$q\quad =\quad Cv$

Where “$q$” is the charge stored over the capacitor and “$v$” is the voltage applied to the capacitor.

## Capacitance:

Capacitance is the capability of a capacitor to store charge. In the above equation, the letter “$C$” is the proportionality constant and representing the capacitance of the capacitor. The unit for capacitance is Farad (named after scientist; Michael Faraday). Capacitance is the property of a capacitor to assess the ability to store charge.

A capacitor would have one Farad capacitance if and only if the voltage applied to it is one volt and it stores charge of one coulomb.

Farad is a very big unit of capacitance, most commonly used units are micro-farad, nano-farad, and pico-farad.

## Capacitance of a Capacitor :

The capacitance does vary from capacitor to capacitor depending upon some factors like the area of the plate, separation between them and the material used.

As the area of plate increases the room for charge storage increases, so it has a direct relationship with capacitance. Where far apart plate can store less charge as compared to close plates, so it has an indirect relationship. Mathematically

$C\quad \propto \quad A\\ C\quad \propto \quad \frac { 1 }{ d } \\ C\quad =\quad \varepsilon \frac { A }{ d }$

Here A is the surface area of the conducting plates (each plate) and d is the separation between the plates. Where $\varepsilon$ is the permittivity of the non-conducting material (dielectric). It measures how easily the dielectric will pass the electric flux lines. The permittivity for vacuumed is represented by $\varepsilon _{o}$and is called absolute permittivity. The value of absolute permittivity is $8.85\times 10^{-12}$F/m. The permittivity for other materials are called relative permittivity and represented by $\varepsilon_{r}=\frac{\varepsilon }{\varepsilon _{o}}$ is the comparison to absolute permittivity. The relative permittivity is also known as the dielectric constant. For every material, there is a threshold if the voltage applied to it is exceeded. The dielectric material will break as an indication of the dielectric strength and called dielectric breakdown voltage.

## Capacitance of a capacitor calculator:

Area of Plate A

Relative Permittivity εr

Distance d

Capacitance C

## Energy stored in a capacitor :

Energy is the ability to do work, where work is moving mass by applying force. In electrical engineering, energy is the ability to move charge by applying voltage.

Storing energy on capacitor means moving charge from one plate to another against the electrical force. To counter the electrical force developed by capacitor charge, an external source i.e. battery is attached to the capacitor in reverse direction. As the charge builds up upon the plates, more and more force is required to move the charge opposite direction. The voltage on the capacitor is directly proportional to the charge on plates.

$V\quad=\quad \frac{q}{C}$

The work to move the element charge from one plate to another is

$dU\quad=\quad Vdq\\ \quad \quad=\frac{q}{C} dq$

To find the total energy stored over the capacitor, we have to integrate the element charge $dq$ up to total charge $Q$.

$U=\quad \int _{ 0 }^{ Q }{ \frac { q }{ C } dq } \\ =\frac { 1 }{ 2 } \frac { Q^{ 2 } }{ C }$

The above formula has also the following variations.

$U \quad = \quad \frac{Q}{2C} \\ = \quad \frac{1}{2} QV \\ = \quad \frac{1}{2} C{V}^{2}$

Charge Q

Capacitance C

Voltage V

Energy Stored U

## Leakage Current :

Until now, we have supposed that conducting plates are separated by insulators and current is not able to pass through it. But practically every material (even insulator) have some free electrons in it. Those minute amount of free electrons is causing a very little current without reaching break down voltage. This low current cause by dielectric impurities is called leakage current which passes through the dielectric of the capacitor.

The leakage current can be ignored for practical purposes. For theoretical calculation, to counter the leakage current, a resistor in parallel with the capacitor is inserted.

## Summary :

A capacitor is a passive electronic component used for storing energy in form of the electrostatic field. Where the capacitance is the ability of a capacitor to store charge. Storing energy means moving charge against the electrical force.

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