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# Capacitor

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 Sub Topics Centuries back, it was already known from electrical experiments that two plates of conducting material, separated from one another in an insulating medium, can receive, store and give out electrical charges. This constitutes the basic principle in a Capacitor. Capacitors are also known as condensers. In the electronics industry, numerous capacitor elements are used in circuit design for control application. These capacitors come in different shapes and sizes. The materials used in the production of these capacitors include aluminum foil, polyester, mica, teflon etc. Electrolytic capacitors are used in certain DC and motor starting applications.

## What is Capacitor?

A capacitor is a two terminal electronic component which store electrical energy with in an electrical field. It consists of minimum two conductors and separated by a dielectric. The main composition of an electrical circuit is by capacitors.

## How Capacitors Work?

Capacitor is made up of two conductors and separated using a non conducting medium known as dielectric. Type of capacitor depends on the selection dielectric materials intern which determines the applications. It is also used for high voltage and low voltage application according to the choice of dielectric.

If the capacitors are connected to a battery, the charge from the negative terminal of the battery flows to the negative terminal of the capacitor. And it is stored using the help of dielectric which is used to separate the two conductors. Main disadvantage of capacitors is we can not store charge for a long period.

## Types of Capacitors

There are different types of capacitors are present according to the dielectric which is used in that. So the application is also different. Each capacitor has its own application sand characteristics.
1. Dielectric Capacitor : It is a variable capacitor. This variations in capacitance is used to tuning transmitters, transistor radios and receivers.
2. Film Capacitor :It is most commonly available capacitors with different dielectrics.
3. Ceramic Capacitors : These are known as disc capacitors because of its shape. It is made up of ceramic disc coated with silver on the both sides. This type is used for very small capacitance.
4. Electrolytic Capacitors : These are widely used one when we required high capacitance. Generally they are used in DC supply circuits because if its high capacitance value and small size.

## Capacitors in Series

As we known, a capacitor consists of two plates. A series connection of capacitors means the second plate of first capacitor is connected by first plate of second capacitor and so on, as illustrated in figure.

In given figure, V is the voltage, q is the charge and C is the capacitance.
We know that,
V = V1 + V2 + V3

$\frac{q}{C_s}$=$\frac{q}{C_1}$+$\frac{q}{C_2}$+$\frac{q}{C_3}$

$\frac{1}{C_s}$=$\frac{1}{C_1}$+$\frac{1}{C_2}$+$\frac{1}{C_3}$

If n number of capacitors are connected in series, the capacitance become,
$\frac{1}{C}$=$\frac{1}{C_1}$+$\frac{1}{C_2}$+$\frac{1}{C_3}$+$\frac{1}{C_4}$+....................+$\frac{1}{C_n}$

## Capacitors in Parallel

Parallel connection is depicted in the given figure. If the capacitors connected parallel, the charge will change according to the capacitance.

So,
q1 = C1V, q2 = C2V, q3 = C3V
q = q1 + q2 + q3
CV = C1V + C2V + C3V
C = C1 + C2 + C3

If there are n number of capacitors connected in parallel, the capacitance become
C=C1+C2+C3+C4+.........+C5

## Capacitor Voltage

Charge, capacitance and voltage of a capacitor are inter related. The relationship between these three parameter is,
Q = CV
So,
V=$\frac{Q}{C}$

From this relation we can conclude that, V is directly proportional to Q and inversely proportional to C.

Capacitor current is defined as the rate of change of charge flow with respect to time.
So, Ic(t) = C$\frac{\mathrm{d}V_{c}}{\mathrm{d} t}$

## Energy stored in a Capacitor

Energy stored in a capacitor is given by,
W=$\frac{1}{2}$$CV^{2}$

Since C = QV,
W=$\frac{1}{2}$QV
where,
W is the energy stored in a Capacitor
C is the capacitance
V is the voltage across the capacitor
Q is the charge on capacitor

## Charging Capacitor

Using the given circuit we can discuss the charging of a capacitor.

Consider the above circuit, let Q and I be the charge on the capacitor and the current in the circuit at time t.
From the circuit diagram,

IR = E - QC...........(1)

If the capacitor get fully charged, the current will be zero.
That is, Q = Q0

∴ E = Q0C ;

(1) becomes,
R$\frac{\mathrm{d} Q}{\mathrm{d} t}$ = ($Q_0$-Q)C

$\frac{dQ}{Q-Q_{0}}$=$\frac{1}{CR}$dt

Integrating and rearranging this equation we get,

Q=$Q_{0}(1-e^{-\frac{1}{CR}t})$.............(2)

Equation (2) represents the charging of a capacitor equation.

## Capacitor Discharge

R $\frac{dQ}{dt}$ + QC = 0
$\frac{dQ}{Q-Q_{0}}$=$\frac{1}{CR}$dt
Q = $Q_{0}e^{-\frac{1}{CR}}$.............(2)