# Dimensions of Emf

## Dimensional Formula of EMF (Electromotive Force)

The dimensional formula of EMF (Electromotive Force) is given by,

M1 L2 T-3 I-1

Where,

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

### Derivation

Electromotive Force, EMF (ε) = Work Done × [Charge]-1.  . . . (1)

Since, Work Done = Force × displacement

= Mass × acceleration × displacement = [M] × [MLT-2] × [L]

Therefore, the dimensional formula of work done = MLT-2 . . . . (2)

And, Charge = current × time

∴ The dimensional formula of charge = IT1 . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Electromotive Force = Work Done × [Charge]-1

Or, ε = [MLT-2] × [IT1]-1 = [M1 L2 T-3 I-1].

Therefore, Electromotive Force or EMF is dimensionally represented as [M1 L2 T-3 I-1].

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