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:

• Dimensions of Temperature
• Dimensions of Wavelength
• Dimensions of Boltzmann Constant
• Dimensions of Kinematic Viscosity
• Dimensions of Rotational Kinetic Energy