Capacitance:is the ratio of the change in an electric charge in a system to the corresponding change in its electric potential. There are two closely related notions of capacitance: selfCapacitanceand mutualcapacitance. Any object that can be electrically charged exhibits selfcapacitance. A material with a large selfcapacitanceholds more electric charge at a given voltage than one with lowcapacitance. The notion of mutualcapacitanceis particularly important for understanding the operations of thecapacitance, one of the three elementary linear electronic components (along with resistors and inductors).capacitor

:Capacitoris a passive two-terminalCapacitorelectrical componentthatstorespotential energy in an electric field.The effect of ais known ascapacitor. While somecapacitanceexists between any two electrical conductors in proximity in a circuit, acapacitanceis a component designed to addcapacitorto a circuit. Thecapacitancewas originally known as a condenser.capacitor

Capacitance & CapacitorTutorial Includes:1. Capacitance 2. Capacitor formulas 3. Factors governing capacitance of a conductor 4. Capacitance of an isolated spherical conductor 5. Potential energy of charged conductor 6. Similarity between a capacitor and spring 7. Sharing of charge between two conductors at different potentials 8. Capacitor and its principle 9. Factor on which capacitor of a capacitance depends 10. Significance of capacitor 11. Charging and discharging of capacitor 12. Capacitance and potential of a capacitor 13. Specific inductive capacity 14. Different types of Capacitors 15. Calculation of capacitance of a parallel plate capacitor 16. Series Combination of capacitor 17. Parallel combination of capacitor 18. Energy stored in charged capacitor 19. Energy stored in series and parallel combination of capacitors 20. Force between the plates of the capacitor 21. Van-de-Graff generator 22. Mathematical Problems of Capacitance and Capacitor 23. Question Answer Notes for Capacitance and capacitor

**What is Capacitance?**

*Capacitance*or

*capacity*of a conductor denotes its ability to hold charge. This ability of a conductor depends on its sizes, shapes, medium and presence of other conductor near it. When a conductor is given a charge its potential rises. It is found that rise of potential is proportional to charge imperted. So if V be the rise of potential of a conductor due to a charge q given to it, then \[q\varpropto V\]

The constant of proportionality is called the capacitance of the conductor.

DefinitionIf in the relationof C (capacitance):q=CVwe putv=1, thenq=C.

Hence, the capacitance of a conductor is numerically equal to electric charge required to raise the potential by one unit.

**: In**

__Units of Capacitance__**SI system**, unit of

**capacitance**is

**Farad (F)**. It is also taken as practical unit of capacitance.

A

**conductor**is said to have**capacitance**of**one Farad**, if**one coulomb charge raises**its*.***electric potential by one volt***i.e.*

**1 F = 1 C. V**

^{-1}
In

**c.g.s**system, unit of**capacitance**is**statfarad.**
A

**conductor**is said to have**capacitance**of one**statfarad**, if**one-statcoulomb****charge raises**its*potential by one statvolt.**i.e.*

**1 Statfarad = Stat Coloumb/stat volt**

Relation between Farad and Statfarad:1F = 1C/1V = 9 x 10^{11 }Statfarad.

**In practice following smaller units of capacitance are also used :**

*microfarad(10*

^{-6}), picofarad(10^{-12})

__Capacitance of a conductor depends on the following factors :__**Surface area of the conductor :**If the surface area of the conductor is large, for a given charge, its potential will be smaller. As \(C \propto \frac{1}{V}\) (fixed charge), so the capacitance increases.-
**Proximity of other conductors :**If another conductor is kept near the given conductor, its rise of potential is less due to a charge given to it. So its capacitance increases. **Nature of the sorrounding medium :**The capacitance of a conductor depends on**dielectric constant**of the medium. Higher the value of*K*(\(K = \frac{\varepsilon }{{{\varepsilon _0}}}\))*K*higher is capacitance of the conductor.

**What is Capacitor?**

A capacitor is a passive two-terminal electrical component that stores potential energy in an electric field. The effect of a capacitor is known as capacitance.

__Factors governing the capacitance of a conductor__**The area of the conductor :**The potential of a conductor decreases with the increase of the surface area of the conductor ; hence its capacitance increases.**The medium surrounding of the conductor :**If air surrounding the conductor is replaced by any non-conducting medium like paraffin, sulphur, glass etc., the capacitance of the conductor increases.**Presence of earth-connected conductor :**If another conductor (uncharged) is placed near the charged conductor under test, specifically if the uncharged conductor is earth-connected, capacitance of the charged conductor under test increases remarkably.

__Capacity of an Isolated Spherical Conductor__- Capacitance of a spherical conductor is directly proportional to its radius.
- The above equation is true for conducting spheres, hollow or solid.
- If the sphere is in a medium, then C = 4Ï€Îµ0Îµr.R
- Capacitance of the earth is 711 Î¼F.

Capacitance of an isolated sperical condcutor

Let us consider a

*Spherical conductor*. Point out its*center*as 'O' and*radius*'r'. Give some*positive charge*say 'q' to charge the conductor. When we will give the charge to the conductor it will start spreading equally over its outer surface. Charge spreading does not depend upon the type of conductor used. One can take both hollow as well as solid conductor. Charge spreading will be same. If the charge spreading will be uniform then the potential will be also uniform.V =q/4Ï€Îµ_{0}r=> C =q/v=> C=q4Ï€Îµ_{0}r/q=> C=4Ï€Îµ_{0}r

We know earth is spherical. So putting the values according to the earth in the above equation.

Lets take the radius r=6400 Km.

So, it becomes 6.4 X 10 6 m.

After substituting the values :

C= Electrostatic figure 2.55 X r

= 6.4 X 10 6/9 X 10 9

=0.711 X 10 -3 farad.

So the value after calculation will be 711 uF.

It is clear from the result that the capacity of the earth is 711 microfarad. The amount 711 farad is very large. Due to such a large capacitance, earth has the ability to carry infinite amount of charge.

__Units__**In esu unit : V = Q/R => C = Q/V = Q/Q/R = R (esu)**

i.e., the capacitance in esu of an isolated spherical conductor placed in air is numerically equal to its radius in cm.

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