Dimensional Formula of Potential Difference

The dimensional formula of potential difference is given by,

[M¹ L² T^-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 = [M¹ L⁰ T⁰] . . . . (3)

Displacement = [M⁰ L¹ T⁰] . . . . (4)

Acceleration = [M⁰ L¹ T^-2] . . . . . (5)

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

Work done = [M¹ L⁰ T⁰] × [M⁰ L¹ T^-2] × [M⁰ L¹ T⁰]

∴ The dimensions of Work done = [M¹ L² T^-2] . . . . (6)

Since, Charge = Current × time

∴ The dimensional formula of charge = [M⁰ L⁰ T¹ I¹] . . . . (7)

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

Potential Difference = work done × [charge]^-1

Or, P.D = [M¹ L² T^-2] × [M⁰ L⁰ T¹ I¹]^-1 = [M¹ L² T^-3 I^-1] .

Therefore, the Potential difference is dimensionally represented as [M¹ L² T^-3 I^-1].

⇒ Check Other Dimensional Formulas:

• Dimensions of Linear Momentum
• Dimensions of Newton
• Dimensions of Kinematic Viscosity
• Dimensions of Linear Density
• Dimensions of Bulk Modulus