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What is the dimensional formula of capacitance?

Answer
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Hint: Capacity is a system 's capability to store an electrical charge. It is given by the ratio of the increase in a system's electrical charge to the corresponding change in its electrical potential.

Complete step-by-step answer:

Capacitors consist of two parallel conductive plates, usually metal, which are prevented from touching each other and separated by a dielectric insulating layer. When an electrical current flow is applied to these pipes, charging one surface with a positive charge and the other plate with an equal and opposite negative charge proportional to the supply voltage. A condenser has the capacity to store an electrical charge Q of electrons.

The capacitor capacity to store this electric charge Q between its plates is proportional to the voltage V applied to a capacitor.

Q=C×V
It can also be written as
Capacitance, C= Charge× Voltage1 ---(i)
We know, Charge = Current × Time
Dimensional formula of charge is [I1T1]---(ii)
Voltage = Electric Field × Distance ---(iii)
Also, Electric field = Force × Charge1

The dimensional formula of force and charge is given by [M1L1T2]
dimensional formula of charge is given by [I1T1]

Hence the dimensional formula for Electric field is

 [M1L1T2]× [I1T1]1
=[M1L1T3I1]--(iv)

In substituting (iv) and (iii) we get,

The dimensional formula of Voltage=[M1L1T3I1]×[L1]=[M1L2T3I1]---(v)

On substituting equation (v) and (ii) in equation (i) we get,

Capacitance = Charge× Voltage1
Hence, C=[I1T1]×[M1L2T3I1]1=[M1L2T4I2]

Therefore, the Capacitance is dimensionally represented as

 [M1L2T4I2]

Note: Once a condenser is fully charged, there is a possible difference between the plates and the greater the area of the plates or the greater the distance between them, the greater the capacitance of the condenser.
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