Dimensional analysis of electromotive force

Steps:

• Electromotive force (emf) has the same units as voltage, the volt (V).
• Volt is defined as joule per coulomb (J/C).
• Joule is kg m² s⁻² from force times distance.
• Coulomb is ampere-second (A s), so V = (kg m² s⁻²) / (A s) = kg m² s⁻³ A⁻¹.

Why B is correct:

• Emf is work per unit charge (from ε = W/q), yielding kg m² s⁻³ A⁻¹ in SI base units.

Why the others are wrong:

• A: s⁻¹ exponent matches inductance, not energy per charge.
• C: Lacks negative exponents and s⁻³, resembling momentum times current.
• D: Omits m and has s⁻¹, akin to force per current.

Final answer: B