Capacitance of a conductor: The electrical capacitance of a conductor is the ability of the conductor to store charge in it.
When a charge is given to a conductor, its potential rises. The actual rise of potential due to this charge will depend upon the size of the conductor and on its position relative to any neighboring conductors. It will also depend upon whether the neighboring conductor is insulated or earthed.
The potential V of the conductor is directly proportional to the charge q given to it.
i.e. q ∝ V
or q = CV
where C is the constant of proportionality and is called the capacitance of the conductor and its value depends on the shape and dimensions of the conductor.
And C = \(\frac{q}{V}\)
Thus capacitance of a conductor may be defined as the ratio of the charge on the conductor to its potential.
If V = 1, then C = q
i.e. capacitance of a conductor is the amount of charge required to raise its potential by unity.
Units:
In S.I., the unit of capacitance is farad,
Since C = \(\frac{q}{V}\)
So, if q = 1 coulomb, V = 1 volt, then C = 1 farad.
Hence, the capacitance of a conductor is said to be 1 farad, if 1 coulomb charge raises its electrical potential by 1 volt
∴ 1 farad = \(\frac{1\ coulomb }{1\ volt }\)
or 1F = \(\frac{1\ C}{1\ V} \) = 1 CV-1
Why farad is very large?
One farad = \(\frac{1\ C}{1\ V} = \frac{C^2}{J} \) [∵ V = \(\frac{J}{C}\)]
J is a convenient unit of energy but coulomb is a very big unit of charge.
Other unit of capacitance is microfarad (µF),
1 µF = 10-6 F
Still smaller unit of capacitance is picofarad (pF),
1 pF = 10-12 F.
