Coulomb (C)

Also called C, Ampere-second

The coulomb is the SI unit of electric charge, defined as the charge carried past a point by a current of one ampere in one second. As static charge it is enormous, worth about 6.25 times 10 to the eighteenth elementary charges.

The definition runs through current. Rearranging the sheet's I=Δq/ΔtI = \Delta q / \Delta t,

1 C=1 A⋅s1\ \text{C} = 1\ \text{A} \cdot \text{s}

so a coulomb is what one ampere delivers in one second. In a circuit that is ordinary: a 0.500.50 A current moves half a coulomb every second, indefinitely.

In electrostatics a coulomb is absurd. Divide by the elementary charge printed on the sheet, e=1.60×10−19e = 1.60 \times 10^{-19} C, and one coulomb is 6.25×10186.25 \times 10^{18} elementary charges. Put two of them one metre apart and Coulomb's law with the AP value k=9.0×109k = 9.0 \times 10^9 gives

F=kq1q2r2=9.0×109 NF = \frac{kq_1q_2}{r^2} = 9.0 \times 10^9\ \text{N}

nine billion newtons, which no benchtop survives. That is why every point charge in an AP electrostatics problem arrives in microcoulombs or nanocoulombs, and why a static answer carrying whole coulombs is usually a prefix nobody converted.

Both scales are real and both use the same unit. They reconcile because a circuit never accumulates charge: it passes charge through and gets it back.

Two symbols, one unit. The AP Physics 2 sheet uses lowercase qq for a point charge and uppercase QQ for the charge on a capacitor plate, and its symbol list defines both as charge. The coulomb measures either.

Coulomb is printed in the unit-symbol tables of the two electricity courses, AP Physics 2 and AP Physics C: Electricity and Magnetism.

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