Do the dimensional analysis of :-
1.Resistance
2. Voltage
Dear student,
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.
Regards