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)

Capacitance is defined as the amount of charge stored per unit voltage, so its SI unit is the farad. To express a farad in base SI units, break down the quantities involved. The charge Q has base units of coulombs, which are ampere-seconds (A·s). The voltage V is energy per charge; since energy is joules (kg·m^2·s^-2) and 1 volt = 1 joule per coulomb, voltage has base units V = (kg·m^2·s^-2) / (A·s) = kg·m^2·s^-3·A^-1. The farad, being Q/V, becomes (A·s) / (kg·m^2·s^-3·A^-1) = kg^-1·m^-2·s^4·A^2. This exact combination corresponds to the farad, the unit of capacitance. The other units have different base-unit expressions (for example, a henry or a coulomb or a volt), so they don’t match this dimensional form.

Capacitance is defined as the amount of charge stored per unit voltage, so its SI unit is the farad. To express a farad in base SI units, break down the quantities involved. The charge Q has base units of coulombs, which are ampere-seconds (A·s). The voltage V is energy per charge; since energy is joules (kg·m^2·s^-2) and 1 volt = 1 joule per coulomb, voltage has base units V = (kg·m^2·s^-2) / (A·s) = kg·m^2·s^-3·A^-1. The farad, being Q/V, becomes (A·s) / (kg·m^2·s^-3·A^-1) = kg^-1·m^-2·s^4·A^2. This exact combination corresponds to the farad, the unit of capacitance. The other units have different base-unit expressions (for example, a henry or a coulomb or a volt), so they don’t match this dimensional form.