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].
Comments