# Capacitor Capacitance Formula Calculator: Capacitor Energy Storage

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 stores energy. The main purpose of the capacitor is to store electric energy for a very short duration of time. The energy storage of the capacitor depends upon the capacitance of the capacitor. The capacitance relates to different parameters by the capacitance formula. 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 from a dielectric (non-conducting material or insulator). There are different types of capacitors available in the market, and all of them have the same fundamental principle.

Practically, the conducting plate may be an 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 $V$ provides charge (electrons) to the plate connected to the negative terminal and the same source takes 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.

## What is Capacitance?

Capacitance is the capability of a capacitor to store charge. In the above equation, the letter “$C$” is the proportionality constant and represents 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 the charge of one coulomb.

## The Capacitance formula:

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

$C\quad \propto \quad A$

$C\quad \propto \quad \frac { 1 }{ d }$

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

Above is the capacitance formula for a capacitor. 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 is 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 the dielectric breakdown voltage.

## The Capacitance Formula Calculator:

The calculator helps in finding the capacitance of a capacitor by using the capacitance formula. Try to put the area of the capacitor plates, the relative permittivity of the dielectric, and the distance between the plates to find the capacitance.

Area of Plate A

Relative Permittivity εr

Distance d

Capacitance C

## Capacitor Energy Storage:

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.

Capacitor energy storage means moving charge from one plate to another against the electrical force. To counter the electrical force developed by the capacitor charge, an external source i.e. battery is attached to the capacitor in the 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 the 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 capacitor energy storage, 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.

$U \quad = \quad \frac{Q}{2C}$

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

## Capacitor Energy Storage Calculator:

To calculate the capacitor energy storage try to input the charge of the capacitor, capacitance, and voltage.

Charge Q

Capacitance C

Voltage V

Energy Stored U

### Leakage Current :

Until now, we have supposed that conducting plates are separated by insulators and the current is not able to pass through them. But practically every material (even insulators) has some free electrons in it. Those minute amounts of free electrons are causing a very little current without reaching break down voltage. This low current caused 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 an electrostatic field. Where the capacitance is the ability of a capacitor to store charge. Storing energy means moving the charge against the electrical force.

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