Dimensions of Resistance

Dimensional Formula of Resistance

The dimensional formula of resistance is given by,

M1 L2 T-3 I-2

Where,

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

Derivation

Resistance (R) = Voltage × Current-1 . . . . (1)

Since, voltage (V) = Electric Field × Distance = [Force × Charge-1] × Distance

The dimensional formula of force = M1 L1 T-2

The dimensional formula of charge = current × time = I1 T1

∴ The dimensional formula of voltage = [Force × Charge-1] × Distance

= [M1 L1 T-2] × [I1 T1]-1 × [L1] = [M1 L2 T-3 I-1] . . . . (2)

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

Resistance (R) = Voltage × Current-1

Or, R = [M1 L2 T-3 I-1] × [I]-1 = [M1 L2 T-3 I-2]

Therefore, resistance is dimensionally represented as M L2 T-3 I-2.

⇒ Check Other Dimensional Formulas:

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