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Capacitance

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Last updated date: 17th Apr 2024
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What is Capacitance?

Capacitance is the ability of a material to accumulate electrical charge. Capacitance, a quantity in the SI system of units, is specified as the ratio of Coulombs to the electrostatic energy stored in a unit volume of the material. Capacitance is the electric property most often associated with the two-dimensional conductor, or condenser, or capacitor. 


However, this property may also be exhibited by a number of other conductors, including thin-film dielectrics, semiconductors, wires and cables, which form so-called distributed capacitances. In practice, the term capacitor is used to describe any storage device which stores a charge in excess of that required to neutralize it. More often than not, a dielectric is involved.  It is the electric part of any capacitor that stores the charge, and the conducting part is the conductor or conductors to which the charge is applied.


A "dielectric" is a material that tends to hold an electric field (electric potential) and can be characterized by a particular permittivity. When a voltage is applied to a dielectric, there are charges (Coulombs) on each side of the dielectric. To remove the charge, the charges have to move to each other, and this is called conduction. If the movement of charges is not free (as it is in a metal), some of the stored energy is converted to heat, and the capacitor will heat up. For that reason, capacitors are often (though not always) of the parallel-plate type: two conductive plates are separated by a dielectric.


An electrical conductor in which movement of the charge carriers is free may store electrical charge without heating up. In such a case, the charges separate from each other, but they are still stored in the material. Such a conductor is not a capacitor: the charge is free to move and the stored energy is the "work done" by the charge on the conductor.


Types 

Capacitors can be classified by the type of dielectric and conductors used. The dielectric can be made of a dielectric fluid or a solid. The dielectric can be of any permittivity, positive or negative. The plates are either of metal, or in some cases, can be of the same metal, separated by an insulator. In parallel-plate capacitors, one plate is insulated from the other and the capacitance is the sum of the charges induced at the two plates. If the plates are connected by a wire, the plates are regarded as one plate, and a capacitor-like circuit is formed with a capacitor in series with the wire.


In Practice, Capacitors Fall into One of Three Categories:

  • Air-Insulated: where there is a separation between the plates, which are separated by a dielectric medium

  • Oil-Immersed: where the plates are immersed in an oil or another dielectric medium and are separated by a thin membrane

  • Oil-Free: where the plates are separated by a vacuum, an electrical insulator.


As a rule, when capacitors have the same electrical charge, they have the same capacitance and the same voltage rating. An exception to this is the voltage rating of the capacitor can be increased with the use of an electrolytic capacitor. This is because an electrolytic capacitor has lower internal resistance than the capacitor's dielectric medium. When charged up, the capacitor's electrolytic medium may form a conducting surface between the plates, allowing current to flow. To ensure that the medium remains a dielectric, it must be immersed in a non-conducting medium such as oil.


Capacitors are Used for Many Purposes:

  • to hold a constant voltage for a specified time, as a charge source for a discharge in a battery or supercapacitor

  • to store or hold energy

  • to reduce voltage spikes or to smoothen it

  • to increase or decrease frequency

  • to increase or decrease high frequency and pulse power

  • to damp out noise (as a low-pass filter, capacitor filters AC noise by passing high frequency AC and blocking low frequency AC)

  • to increase or decrease the impedance of AC circuits (as a load capacitor, inductor or resistor) to protect electronic circuits (as a bypass capacitor, snubber or crowbar)


Capacitance in mH/mF is Commonly Used to Describe the Capacity of a Capacitor:

  • A 2 µF (0.002 Farad) capacitor has a capacitance of 2 µF,

  • A 0.02 µF (2 mF) capacitor has a capacitance of 0.02 mF,

  • A 2 µF (2 mF) capacitor has a capacitance of 2 µF.

  • A 1 nF (10 µF) capacitor has a capacitance of 1 nF.

Capacitance can be calculated using a formula, given in Farads and Microfarads, which means A micro farad (µF) is an abbreviation for microfarad (10−6 Farad), the SI unit of capacitance. It is also called a microfarad. Its symbol is "µ".


Farads and Microfarads

Farads are derived from the Greek word , fars, meaning distance. "F" in Farads means far, or distance. Thus Farads measure the distance between two plates of a capacitor and can be expressed as the capacitance (in terms of F) divided by the distance (in terms of units) between the plates. For example, a 5 pF capacitor has a capacitance of 5 pF and an inter-electrode distance of . It would be expressed as  (5 pF/ )( or ) = 5 pF.


Farads are used primarily to measure the ability of a capacitor to withstand a voltage of a given magnitude. A capacitance of 5 pF would be able to withstand a voltage of 5 V. A 10 pF capacitor would be able to withstand a 10 V voltage. These units of measurement are used primarily for safety purposes, as they can be converted to SI-units with the aid of multiplication factors. 


When it is possible to find safety precautions to use the "per mille" safety factor in the case of measuring devices that are not critical, the safety factor can be multiplied to get the value in SI units.  The capacitance is multiplied by the safety factor. Thus a device with 1 µF of capacitance would be recommended to use a safety factor of  in order to be safe (as the capacitance is multiplied by the safety factor which can be expressed as an SI unit, this will lead to the 1 µF in the end).   


The result of the multiplication is multiplied by the voltage to get the voltage with which the capacitance can be charged.   Therefore, if a device with 1 µF of capacitance is charged to a voltage of 50 V (which is safe by itself, but might not be advisable with a device like a car, where high voltages may be dangerous), the resulting voltage is 50V×1/1,000 = 5 V. 


This number is then divided by the distance between the plates. The resulting number, divided by the distance, is then multiplied by the safety factor.  In this example it would become 5V/ = 5 V/ (5 pF/(or )) = 1 V/(pF).  The device may be recharged up to 100 V and will withstand a 10 V charge before failure.  It is assumed the capacitance is not damaged and may be recharged to a full 100 V.


Sometimes when you switch on the fan, it doesn’t move.

 

You try to rotate the fan by giving an external force or a torque via your hands to make it rotate then you call an electrician to get this issue resolved. The electrician tells us that the condenser isn’t functioning properly. Well, this condenser is nothing but the Capacitor.

 

On this Page, We’ll Learn the Following Things:

  • Capacitance

  • Unit of capacitance

  • SI unit of capacitance

  • Unit of electrical capacitance

Capacitance

The capacitance of a capacitor is defined as the ratio of the charge on the capacitor to the potential of the capacitor.

 

The electric field in the region between the conductors is directly proportional to the charge Q.

 

The potential difference B = Work done per unit positive charge in taking a small test charge against the electric field.

 

Therefore, B is proportional to Q. 

 

Hence the ratio Q /B  must be constant,

 

i.e.,

Q/ B = constant = H

 

The constant H is called the Capacitance of the capacitor and it doesn’t depend upon Q and B.

 

The capacitance depends on the shape, size, and geometrical placing of the conductors and the medium between them.

 

Potential of Capacitor

The charge spread on the positive plate is called the charge on the capacitor.

 

The potential difference between these two plates is called the potential of a capacitor.

 

A capacitor is a combination of two metallic plates separated by an insulating medium where the magnitude of the positive charge spread on one plate (i.e. positive plate) equals the magnitude of the negative charge on the other plate (i.e. negative plate).

 

Let’s say the charge induced on one plate is +P and the potential difference is A+  and on the other, it is -N and a potential difference developed is A’

 

So, the net charge on the capacitor will be: Q = +P - N = 0.

 

The potential difference between these two plates: B = A - A’

 

The term charge doesn’t mean the total charge on a capacitor.

 

Unit of Capacitance

The S.I unit of capacitance (H) is coulomb/volt which is written as farad. 

 

If Q = 1 coulomb and

 

V = 1 volt, 

 

then H = 1 farad.

S.I. the base unit of H = s4⋅A2⋅m-2⋅kg-1

Dimensional formula for H = M-2L-2T4 I2

 

The capacitance of a conductor is said to be one farad when one coulomb of charge raises its potential via one volt.

 

This symbol For farad is a large unit on normal scales and microfarad (mF) is used more frequently.

 

Smaller Units of Capacitance

1mF =  10- 6 farad

1 nF = 1nF = 10- 9 farad

1 mF = 1 m mF = 1 pf = 10-12 farad

 

The capacitance of a spherical conductor

 

An isolated charge conducting sphere has a capacitance which means a charged sphere has stored some energy as a result of being charged. 

 

The potential of the inner sphere:

 

Ba = Q / 4 x π x μo x e - Q / 4 x π x μo x f 

 

Here, Ba is the potential generated at the inner sphere A.

 

e =  Radius of the inner sphere.

 

μo =  Permittivity of free space (The proportionality constant that specifies the strength of the electric force between electric charge in a vacuum).

 

f =  Radius of the outer sphere B.

 

The outer sphere B is earthed so potential at Bb = 0. 

 

Value of μo = 8.85 x 10-12 C 2 N-1 m- 2 

 

 1/  4 x π x μo = 9 x 109 

 

The potential difference, B = Ba - Bb 

 

 =  Q x (1/ 4 x π x μo x e  - 1/ 4 x π x μo x f) 

 

=  Q/ 4 x π x μo x (f - e) / e x f

 

Since B = Q / 4 x π x μo and Q = H x B

 

For an isolated spherical sphere:

 

\[ H = 4 \times \pi \times  \frac{\mu_{0}}{\frac{1}{e}} - \frac{1}{f} \], and taking e as R and b -----> ∞

 

We get that: 

H = 4 x π x μo x R

 

The Capacitance of the Cylindrical Capacitor

A cylindrical capacitor consists of two coaxial cylinders of the same length l and radius R1 and R2.

 

The outer cylinder of radius R2 is earthed and the inner cylinder of radius R1 is given some charge.

 

The capacity of a cylindrical air conductor is given by

H = 2 x π x μo x l / loge (R2 / R1)

 

The capacitance of the parallel plate capacitor

 

The electrical intensity (S) between two plates is given by  

 

S = σ / A = 1 / μo Q / A x d

 

Since  B = S x d = 1/ μo x Q/ A x d

 

H = Q / B = Q / 1/ μo x Q/ A x d = μo x A/ d

 

Where H =capacitance

 

B= The potential difference between the two plates

 

Q =  The charge generated at plate 1 and plate 2.

 

σ = Surface charge density

 

A =  Area of each of the two plates separated by a distance d.

H = μo x A/ d


Summary

We observed that when the capacitor is given a charge through an external source or a battery, the charge accumulates on the two plates, and as soon as we connect this capacitor to the circuit the electric current ‘i’ starts flowing in the opposite direction of the electrons. The negative charge would go towards the positive charge, and the charge on the plate would get neutralized.

FAQs on Capacitance

1. Calculate the capacity of Earth taking it as a sphere of radius 6500 km.

To find M

R = 6500 km 

H =  4 x π x μo x R = 1/ 9 x 10 9 x 6.5 x 106


H = 7.2 x 10- 4 F

2. Calculate the capacitance (H) of a parallel plate capacitor with the area of each plate 2 cm 2 and separation of 4 mm.

Here, A = 2 cm 2 = 10- 4  m2

           d = 4 mm = 4 x 10 - 3  m

           μo = 8.85 x 10 -12 C 2 N-1 m- 2

H = μo x A / d = 8.85 x 10 -12 x  2 x 10-4 / 4 x 10-3

On solving we get: 

              

H = 4.425 x 10 -13 F =  4,425 x 10-7 mF

3. What is the physical significance of capacitance?

Capacitance of an arrangement tells us the potential to which an arrangement will be raised when a given charge is placed on it. For a given charge, smaller the potential, larger must be the capacitance and vice-versa.

4. A boy entered a big metallic cage supported on insulating pillars and then charged the cage with a powerful electric machine. He remained safe inside the cage. Do you believe this is happening?

Yes, the cage is insulated, the entire charge remained on the outer surface of the cage and potential at all points also remained the same which means there was no potential difference between any two points in the cage, the boy didn’t get the shock and remained safe inside the cage.

5. Define Capacitance.

The capacitance of a capacitor is defined as the ratio of the charge on the capacitor to the potential of the capacitor. The electric field in the region between the conductors is directly proportional to the charge Q. The potential difference B = Work done per unit positive charge in taking a small test charge against the electric field. Therefore, B is proportional to Q. Hence the ratio Q /B  must be constant,


Q/ B = constant = H

 

The constant H is called the Capacitance of the capacitor and it doesn’t depend upon Q and B.

6. What is potential capacitance ?

The charge spread on the positive plate is called the charge on the capacitor. The potential difference between these two plates is called the potential of a capacitor. A capacitor is a combination of two metallic plates separated by an insulating medium where the magnitude of the positive charge spread on one plate (i.e.positive plate) equals the magnitude of the negative charge on the other plate (i.e. negative plate).

7. What is the unit of capacitance? 

The S.I unit of capacitance (H) is coulomb/volt which is written as farad. 

If Q = 1 coulomb and

V = 1 volt, 

then H = 1 farad.

S.I. the base unit of H = s4⋅A2⋅m−2⋅kg−1

Dimensional formula for H =M−1L−2T4I2

The capacitance of a conductor is said to be one farad when one coulomb of charge raises its potential via one volt.

 

This symbol For farad is a large unit on normal scales and microfarad (mF) is used more frequently.

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