# Dimensions of Potential Difference

## Dimensional Formula of Modulus of Rigidity

The dimensional formula of modulus of rigidity is given by,

[MLT-3 I-1]

Where,

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

### Derivation

Potential Difference = work done × [charge]-1 . . . . (1)

Since, Work done = Force (M × a) × Displacement . . . (2)

And, the dimensional formula of,

Mass = [MLT0] . . . . (3)

Displacement = [MLT0] . . . . (4)

Acceleration = [MLT-2] . . . . . (5)

On substituting equation (3), (4) and (5) in equation (2) we get,

Work done = [MLT0] × [MLT-2] × [MLT0]

∴ The dimensions of Work done = [M1 LT-2] . . . . (6)

Since, Charge = Current × time

∴ The dimensional formula of charge = [MLT1 I1] . . . . (7)

On substituting equation (6) and (7) in equation (1) we get,

Potential Difference = work done × [charge]-1

Or, P.D = [M1 LT-2] × [MLT1 I1]-1 = [MLT-3 I-1] .

Therefore, the Universal Gravitational Constant is dimensionally represented as [MLT-3 I-1].