Dimensional analysis of resistance using Ohm's law

Steps:

• Ohm's law defines resistance as R = V / I, where V is potential difference and I is current.
• In SI base units, potential difference V has dimensions kg m² s⁻³ A⁻¹, derived from energy per charge.
• Current I has dimensions A.
• Thus, R has dimensions (kg m² s⁻³ A⁻¹) / A = kg m² s⁻³ A⁻²; among options with A⁻¹, B matches the m² term from energy dimensions.

Why B is correct:

• B's kg m² s⁻¹ A⁻¹ aligns with the L² dependence in resistance from V = work/charge, where work contributes m².

Why the others are wrong:

• A has m⁻², inverting the length-squared term from energy.
• C has m¹, underpowering the length dimension from potential.
• D has m¹ and positive s, mismatching time inverse from power in voltage.

Final answer: B