Let I = current through a conductor, R =its resistance and V = potential difference across its ends. According to Ohm's law, product of two of these quantites equals the third. Obtain Ohm's law from dimensional analysis. Dimensional formula for R and V are `[ML^2 T^(-3) A^(-2)] and [ML^2 T^(-2) A^(-1)]` respectively.

Explanation

Let `V = I^a T^b`
`:. [ML^2 T^(-3) A^(-1)] = A^a [ML^2 T^9-3) A^(-2)]^b = M^b L^(2b) T^(-3b) A^(a-2b)`
Applying the principle of homogeneity of dimensions, we get
b = 1, 2b = 2, -3b = -3
a-2b = -1, a = -1 +2b = -1+ 2 =1
Putting these values in (i), we get
`V = I^1R^1`
This is Ohm's law.