A derived unit is made by combining SI base units, using the equation that defines the quantity. Many derived units have their own names, but each can always be written in base units.• newton: F = ma, so 1 N = 1 kg m s−2
• joule: work = force × distance, so 1 J = 1 N m = 1 kg m2 s−2
• watt: power = energy / time, so 1 W = 1 J s−1 = 1 kg m2 s−3
• pascal: pressure = force / area, so 1 Pa = 1 N m−2 = 1 kg m−1 s−2
• coulomb: Q = It, so 1 C = 1 A s
• volt: V = W/Q, so 1 V = 1 J C−1 = 1 kg m2 s−3 A−1Worked example: show that the volt is kg m2 s−3 A−1. Start from V = P/I:V = W A−1 = (kg m2 s−3) A−1 = kg m2 s−3 A−1 Base units let you check that an equation is homogeneous, meaning both sides have the same base units. For Ek = ½mv2, the right side is kg × (m s−1)2 = kg m2 s−2, which matches the joule. Pure numbers such as ½ have no units, so a homogeneous equation can still have a wrong numerical factor. A non-homogeneous equation must be wrong.
• joule: work = force × distance, so 1 J = 1 N m = 1 kg m2 s−2
• watt: power = energy / time, so 1 W = 1 J s−1 = 1 kg m2 s−3
• pascal: pressure = force / area, so 1 Pa = 1 N m−2 = 1 kg m−1 s−2
• coulomb: Q = It, so 1 C = 1 A s
• volt: V = W/Q, so 1 V = 1 J C−1 = 1 kg m2 s−3 A−1Worked example: show that the volt is kg m2 s−3 A−1. Start from V = P/I: