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Suganya Sukumar
Mar 14, 2019

A capacitor is one of the important and basic electronic devices that is used for various purposes. Here's some information that will help you in understanding how capacitors work.

Capacitor is a simple electronic device that is used to store electric charge. It consists of two metal plates separated by a dielectric in between. The dielectric material between the plates can be air or any insulator.

The capacitance of this device is given by the formula:

**C = ( ɛ**_{0} ɛ_{r} A )/d

where,

where,

- ɛ
_{0}is the permittivity in free space, which is approximately equal to 8.85 × 10^{-12}F/m, - ɛ
_{r}is the dielectric constant or relative permittivity, - A is the area of the plates and
- d is the distance between the plates

The unit of capacitance is generally microfarad (µF), nanofarad (nF), picofarad (pF) and for super-capacitors the unit of capacitance is Farad (F). The capacitance is directly proportional to the area of the plates and the dielectric constant (nature of medium in between the plates) and inversely proportional to the spacing between the plates.

The capacitance (C) is also defined as the ratio of electric charge (Q) to the potential difference (V), between the plates. (1 coulomb = 6.25 × 10^{18} electrons)

**C = Q/V**

Let us consider a neutral metallic plate P1 and supply a positive charge of magnitude q coulomb, until its potential rises to a maximum of V. Let us place another parallel plate P2, near and parallel to the metal plate P1.

Due to the phenomenon of electromagnetic induction, negative charges are induced at the near end of the metal plate P2 and consequently equal number of positive charges are separated out at the other end of the plate P2. Let us connect the plate P2 to the earth so that the positive charges on the plate P2, flow to the earth.

Now even after connecting the plate P2 to the earth, negative charges on the plate P2 remains there only. This is because, the negative charges on P2 are strongly attracted by the positive charges on the metal plate P1.

Due to the presence of the negative charges on the metal plate P2, the potential on the metal plate P1 is decreased, because the negative charges in the plate P2 neutralizes the positive charge on P1.

So as to come back to the initial stage, that is when the metal plate P1 was having a maximum potential of V, the metal plate P1 imports a large number of positive charges. Thus, in this way, the capacitance is increased, and a capacitor is formed.

Breakdown voltage is the maximum voltage that can be applied across this device and if the voltage is increased beyond the breakdown voltage, the insulator (dielectric) between the plates of this electronic device will break and the device will begin to conduct.

The reactance (X_{c)} offered by such a device is given by the formula below.

X_{c} = 1 / wC = 1 / 2 π f C

where,

X

where,

- π is 22/7,
- w is the resonant frequency,
- f is the frequency and
- C is the capacitance

We know that the frequency of direct current (DC) is zero. So, by substituting the value of zero frequency to the above equation, the value of reactance is infinite. This means that, the reactance offered by the device to a DC signal is infinite and so it does not allow DC to pass through it.

It passes AC (Alternating Current), because AC has a frequency value which is not equal to zero. It will be more clear from the following substitution.

X_{c} = 1 / wC

= 1 / 2 π f C

= 1 / 2 × π × 0 × C

= 1 / 0

= infinity

X

= 1 / 2 π f C

= 1 / 2 × π × 0 × C

= 1 / 0

= infinity

Before understanding how the total value of capacitors is calculated, it is necessary to know a few points.

✦ The mathematical equation of Ohm's law is I = V/R, where, I is the current flowing in the circuit, V is the voltage and R is the resistance offered by the element in the circuit. Replacing the resistance with capacitor, the formula is derived.

✦ The mathematical equation of Ohm's law is I = V/R, where, I is the current flowing in the circuit, V is the voltage and R is the resistance offered by the element in the circuit. Replacing the resistance with capacitor, the formula is derived.

✦ AC (alternating current) signal is passed through the circuit containing the capacitors. So, dv/dt which is used as the frequency of the signal varies.

The current passing through the circuit is denoted by i. Here, voltage changes but current remains the same.

By using Ohm's law,

i=C_{1} (dv_{1}/dt); i=C_{2}(dv_{2}/dt)

i(1/C_{1}+1/C_{2})=d(v_{1}+v_{2})/dt

i= (C_{1}.C_{2} / (C_{1}+C_{2})dv/dt

Thus, C_{series}=(C_{1}.C_{2})/ C_{1}+C_{2}

By using Ohm's law,

i=C

i(1/C

i= (C

Thus, C

The current passing through C_{1} is i_{1} and the current passing through C_{2} is i_{2}. In this connection, the voltage remains the same, but the current varies. By Ohm's law,

i_{1}=C_{1} dv/dt, i_{2}=C_{2} dv/dt and the total current i= i_{1}+i_{2}=(C_{1}+C_{2})dv/dt Thus, C_{parallel}= C_{1}+C_{2}

i

- As this device can block DC, it can be used as a filter in some electronic circuits.
- It can withstand any change in voltage applied, as it can charge and discharge at any time.

- They are used in a rectifier circuit (converts AC to DC) to remove the unwanted ripples in the output.
- It couples with the noise in the radio receiver circuit, thereby avoiding any disruption in the output.

This device is even used to filter out the ripples in the DC signal. There are various types of capacitors that are used to store energy. The charging and discharging mechanism of this device is similar to the mechanism of a water tank. When the water is filled in a tank, it overflows. Similarly when it is charged completely, it discharges.