Capacitor

Introduction

Capacitor is a device which stores electrical energy. Capacitor is a system of two-conductors which carries charges of opposite sign but of equal magnitudes and separated by an insulating medium. The insulating area is either an electric insulator or vacuum like glass, paper, air,  semiconductor or dielectric.

Uses of Capacitor

1. Capacitors are used for storing electric potential energy like batteries.
2. Capacitors are also used for filtering the unwanted frequency signals.
3. Capacitors are applicable in delaying voltage changes when coupled with resistors.
4. Capacitors also work as a sensing device.
5. Capacitors are used in the audio system of vehicles.
6. Capacitors are used for the separation of AC and DC.

Capacitors have two conductors in which one has a positive charge +Q and potential +V whereas the second conductor has negative charge -Q with the same magnitude and the potential is –V.

Charge on Capacitor

The total charge on the capacitor is 0 (zero) because it has two charges of the same magnitude but different direction.

Therefore, -Q+Q=0

Capacitance

Capacitance is defined as the ratio of change in the electric charge of a system to the change in the electric potential of that charge.

The conducting plates have some charges q1 and q2  (generally when one plate has +q then the other plate has -q charge). The electric field which lies in the region between the plates depends on the charge given to the conducting plates. We also know the potential difference (V) is proportional to the electric field so we conclude that,

QV

Q=CV

C=Q/V

Here, 

Q =charge 

V =potential difference

C = Capacitance

Depending on the use of the capacitor, the capacitance of the capacitor can be fixed or it may be variable. From the equation of capacitance, we see that ‘C’ depends on charge and voltage. It actually depends on the shape and size of the capacitor and also the medium between the conductive plates.

Energy Stored in a Capacitor

When the opposite charges have been placed on either side of a parallel plate capacitor then the charges can be used to do work by allowing the charges to move towards each other through a circuit. Total energy which is extracted from a fully charged capacitor is given as:

U=1/2 CV2

Capacitors work in a similar way to rechargeable batteries. The main difference between a capacitor and a battery is the technology they use to store energy. Unlike batteries, the capacitor’s ability to store energy does not rely on chemical reactions but on physical design. This allows it to keep positive and negative charges separate.

Standard Units of Capacitance

The standard unit of capacitance is Farad. But Farad is a big unit for practical purposes. Therefore, capacitance is generally measured in the sub units of Farads like microfarads (µF) or pico-farads (pF).

Mostly electrical and electronic applications are covered by the following standard units of capacitance (SI) which makes the calculations easy.

1 mF (millifarad)=10-3 F

1 F (microfarad)=10-6 F

1 nF (nanofarad)=10-9 F

1 pF (picofarad)=10-12 F

Capacitance of a Parallel Plate Capacitor

The parallel plate capacitor has two similar conducting plates and these two plates have a surface area A and distance between them is d. Charge Q is stored by the plates when voltage V is applied to the plates.

The force between the charges increases with the charge values ​​and decreases with the separation distance. When the plates are larger then, they store more charge. Therefore, the value of C is larger for a big value of A. The closer the plates are, the greater the attraction of opposite charges on them. Hence C is larger for smaller d.

Formula for the charge density on the plates is

=Q/A

Here, 

= Charge density

Q =charge 

A = area

When the separation distance (d) is small then the electric field between the plates is uniform and the magnitude is given as

E=/0

When the electric field between the plates becomes uniform then the potential difference between the plates is

=Ed=d/0=Qd/0A

Now put these values in the capacitance formula we get

C=Q/A=Q/Qd/0A

C=0(A/d)

Capacitance of a Spherical Capacitor

Spherical capacitors contain two concentric conducting spherical shells having radii R1 and R2. The charges on the shells are equal and directions are opposite as +Q and –Q respectively. The electric field which lies between shells is directed radially outward. The magnitude of the field can be determined by using Gauss law over a spherical Gaussian surface having radius r concentric with the shells.

When the enclosed charge is +Q then

E.ndA=E(4r2)=Q/0

Electric field between the conductor is

E=1/40Q/r2 r

Integrate it we get

V=R1R2E.dl=Q/40(1/R1-1/R2)

Potential difference between two conductors is

VB–VA=ABE. dL

Potential difference between two plates is

V=-(V2–V1)=V1–V2

Now put these values in capacitance formula then,

C=Q/V=40 R1R2/R2–R1

Isolated Capacitor

An isolated capacitor is one that is not connected to the rest of the circuit and hence cannot be charged or discharged.

Factors Affecting the Capacitance

1. Capacitance depends on the shape and size of the conductor.
2. Capacitance also depends on the medium between the two conductors.
3. Capacitance is affected by the presence of other conductors close to it.

Conclusion

Capacitor is a device which stores electrical energy. Capacitor is a system of two-conductors which carries charges of opposite sign but of equal magnitudes and separated by an insulating medium. The insulating area is either an electric insulator or vacuum like glass, paper, air, semiconductor or  dielectric.

Capacitance is defined as the ratio of change in the electric charge of a system to the change in the electric potential of that charge.

Total energy which is extracted from a fully charged capacitor is given as:

U=1/2 CV2

The standard unit of capacitance is Farad.

1 mF (millifarad)=10-3 F

1 F (microfarad)=10-6 F

1 nF (nanofarad)=10-9 F

1 pF (picofarad)=10-12 F