Prove that: Unit of electric resistance, ohm (Ω) = kg·m²·s⁻³·A⁻².

Question

Accepted Answer

By Ohm's law, Resistance R = V / I, where V is potential difference (voltage) and I is electric current. Unit of voltage V = Joule/Coulomb = (kg·m²·s⁻²) / (A·s) = kg·m²·s⁻³·A⁻¹ [since 1 Coulomb = 1 Ampere × 1 second, and 1 Joule = kg·m²·s⁻²]. Unit of current I = A (ampere). Therefore, unit of R = V/I = (kg·m²·s⁻³·A⁻¹) / A = kg·m²·s⁻³·A⁻². Hence proved: Ω = kg·m²·s⁻³·A⁻².