Dimensional Analysis of Electrical Resistance

Steps:

• Ohm's law states resistance R = V / I, where V is voltage and I is current.
• Voltage V derives from energy per charge: V = (kg m² s⁻²) / (A s) = kg m² s⁻³ A⁻¹.
• Current I has unit A.
• Divide: R = (kg m² s⁻³ A⁻¹) / A = kg m² s⁻³ A⁻².

Why D is correct:

• D matches the SI base unit expression for the ohm, Ω = kg m² s⁻³ A⁻², from the definition R = V/I.

Why the others are wrong:

• A: Wrong length exponent (m⁻² instead of m²) and omits time (s⁻³).
• B: Omits time dependence (missing s⁻³).
• C: Incorrect length (m instead of m²) and current (A² instead of A⁻²).

Final answer: D