# Dimensions of Electric Potential

## Dimensional Formula of Electric Potential

The dimensional formula of electric potential is given by,

[M1 LT-3 I-1]

Where,

• M = Mass
• I = Current
• L = Length
• T = Time

### Derivation

Since, Potential energy = Charge of particle × Electric potential

Therefore, electric potential =  Potential energy × [Charge of a particle]-1 . . . . (1)

Since, electric charge = electric current × time

∴ The dimentional formula of electric charge = [I1 T1] . . . . . (2)

Since, Potential Energy = M × g × h . . . . . . (3)

The dimensions of height (h) and Mass (M) = [M0 LT0] and [M1 LT0] . . . . (4)

And, the dimensional formula of acceleation due to gravity (g) = [M0 LT-2] . . . . (5)

On substituting equation (4) and (5) in equation (3) we get,

Potential Energy = [M1 LT0] × [M0 LT-2] × [Mo LT0]

Therefore, the dimension of potential energy = [M1 LT-2] . . . . (6)

On substituting equation (2) and (6) in equation (1) we get,

Electric potential =  Potential energy × [Charge of particle]-1

Or, Ep = [M1 LT-2] × [I1 T1]-1 = [M1 LT-3 I-1]

Therefore, the electric potential is dimensionally represented as [M1 LT-3 I-1].