Kg^-1 m^-2 s^4 A^2 is the base SI unit for which quantity?

Kg^-1 m^-2 s^4 A^2 is the base SI unit for which quantity?

• A. Henry
• B. Farad
• C. Coulomb
• D. Volt

Answer: (B)

Dimensional analysis shows which derived unit matches that combination of base units. A coulomb is A·s and a volt is joule per coulomb; a joule is kg·m^2/s^2, so volt equals kg·m^2/(s^3·A). A farad, being a coulomb per volt, becomes (A·s) / (kg·m^2/(s^3·A)) = A^2·s^4 / (kg·m^2) = kg^-1·m^-2·s^4·A^2. The given unit matches this exactly, so it represents capacitance, i.e., a farad.

Dimensional analysis shows which derived unit matches that combination of base units. A coulomb is A·s and a volt is joule per coulomb; a joule is kg·m^2/s^2, so volt equals kg·m^2/(s^3·A). A farad, being a coulomb per volt, becomes (A·s) / (kg·m^2/(s^3·A)) = A^2·s^4 / (kg·m^2) = kg^-1·m^-2·s^4·A^2. The given unit matches this exactly, so it represents capacitance, i.e., a farad.