Let I represent the current through a conductor, R its resistance, and V the potential difference across its ends. According to Ohm's law, the product of two of these quantities is equal to the third. Determine Ohm's law using dimensional analysis. The dimensional formulae for R and V are ML^2 I⁻² T⁻³ and ML^2 T⁻³ I⁻¹ respectively.

Step-by-step solution

The dimensional formula for potential difference V is [M L^2 T⁻³ I⁻¹] . The dimensional formula for resistance R is [M L^2 T⁻³ I⁻²] . The dimensional formula for current I is [I] . Checking the dimensions of the product IR : [I][R] = [I] [M L^2 T⁻³ I⁻²] = [M L^2 T⁻³ I⁻¹] This matches the dimensional formula for V . Checking the other relations: [I][V] = [I] [M L^2 T⁻³ I⁻¹] = [M L^2 T⁻³] [R] [V][R] = [M L^2 T⁻³ I⁻¹] [M L^2 T⁻³ I⁻²] = [M^2 L^4 T⁻⁶ I⁻³] [I] [I^2][R] = [I^2] [M L^2 T⁻³ I⁻²] = [M L^2 T⁻³] [V] Thus, the