Capacitance

Description:

Capacitance can be understood more clearly, with the help of an analogy. Let there be two tanks T₁ and T₂ where T₁ is a narrow tank as compared to T₂. Let each tank T₁ and T₂ contains 5 litres of water. The level of water in both the tanks reaches as 5 cm  and 2 cm respectively.

Direction of F low (T₁ – T₂)

height of water in (T₁ > T₂)

i.e T₁ requires 1 litre of water to raise 1cm whereas T₂ requires 2.5 litre to reach the same height. The total amount of water that can be stored in a tank is the capacity of the tank, whereas the amount of water requited to raise the level by a unit length is its capacitance.

If tanks are connected together, then, even though the volume of water in T₂ is more than in T₁, still water will flow from tank T₁ to T₂ as the height of water in T₁ is greater than in T₂. So, height of water within the tank is the deciding criteria for the direction of flow. The flow will stop when water level of both the tank becomes equal.

Similarly, potential of a conductor is the deciding criteria for direction of flow of charges.

Potential − Potential of a conductor is the total amount of work done in moving a unit charge within conductor.

Let there be two conducting metals (M₁ and M₂), each consist of 5 coulomb of charge. Let the potential of metals due to theses charges be 5V and 2V respectively.

For metal M₁:

For 5 volt raise in potential, charge required = 5 coulomb

So, For 1 volt raise in potential, charge required = 1 coulomb

For metal M₂:

For 2 volt raise in potential, charge required = 5 coulomb

so For 1 volt raise in potential, charge required = 2.5 coulomb

So the ratio of charge required to raise the potential of metals M₁ and M₂ respectively by unit volt is 1: 2.5

Similarly,  if there is a metal, which is given charge ‘q’ to raise the potential by ‘V’ volts

Then, for 1 volt raise in potential, charge required = q/v coulomb

This amount of charge is the capacitance of metal.

Capacitance

Capacitance of a conductor is amount to a charge required to raise its potential by 1 volt. It is symbolized by C.

C = q/v

If potential is 1 in that case C=q

Unit of capacitance

• SI unit is Farad (f).
• Practical unit is micro Farad (μf).
• 1 μf = 10^-6f

1 Farad

1 farad is the capacitance of that capacitor, whose potential is raised by 1 volt when charge of 1 coulomb is given to it.

1 farade = 1coulomb/1 volt