Electrical Capacitance of A Conductor-

 

The electrical capacitance of a conductor is a measure of its ability to store electric charge or energy.

 

It is a positive scalar quantity.

 

Capacitance Formula-

 

When a conductor is given some charge, it acquires a certain electric potential.

More is the charge on a conductor, more is the electric potential of it.

 

If a charge Q is put on a conductor which raises its potential by V, then-

Or we can write-

 

where C is a constant of proportionality called as electrical capacitance of the conductor.

 

From here, we have-

 

OR

 

If V = 1 unit, then C = Q. Thus,

 

The electrical capacitance of a conductor may be defined as the charge required to raise its potential by a unit amount.

 

Factors Affecting Capacitance-

 

The capacitance of a conductor depends upon the following factors-

• shape and size of the conductor
• nature (permittivity) of the surrounding medium
• presence of the other conductors in its neighborhood

 

It is worth noticing that the capacitance of a conductor does not depend on the-

• nature of material of the conductor
• amount of charge existing on the conductor

 

SI Unit of Capacitance-

 

The SI unit of capacitance is farad (F).

 

1 F = 1 C V^-1

The capacitance of conductor is said to be one farad if one coulomb of charge is required to raise its potential by 1 volt.

 

It is important to note that one farad is a very large unit of capacitance. Other smaller and practical units of capacitance are-

• 1 micro farad (μF) = 10^-6 F
• 1 nano farad (nF) = 10^-9 F
• 1 pico farad (pF or μμF) = 10^-12 F

 

Dimensional Formula of Capacitance-

 

The dimensional formula of capacitance is [M-1L-2T4A2].

 

It can be derived as-

 

 

Also Read- Deriving Dimensional Formula of Electric Potential

 

Read the next article on-

Capacitance of Isolated Spherical Conductor

 

Get more notes & other study material of the Chapter Electrostatic Potential & Capacitance.