Circuits & Electrical Power · Charge in motion
The ampere is a rate
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The ampere is a rate

A current is not a substance. It is a rate — the rate at which charge crosses a section of conductor — and once you hold that, Q=ItQ = I t stops being a formula to memorise and becomes a definition to read.

Read aloud: Q equals I t. QQ is the charge that has passed, in coulombs; II is the steady current, in amperes; tt is the duration of the flow, in seconds. Solve it for the charge going forward, for I=QtI = \dfrac{Q}{t} when the charge and the clock are known, or for t=QIt = \dfrac{Q}{I} when you are asking how long a process must run. Note the steadiness clause: if the current varies, this relation gives you the AVERAGE, and the honest version needs calculus.

Now the trap this lesson exists for. Batteries are not rated in coulombs; they are rated in milliamp-hours or amp-hours, because that is what a user understands. An amp-hour is Q=ItQ = I t with the clock in hours, so converting it back to coulombs costs you two multiplications and not one: ×103\times 10^{-3} to turn milliamps into amps, then ×3600\times 3600 to turn hours into seconds. A 2000 mA·h cell is 2 A·h, and 2 A·h is 7200 C. Students who pay one of those two tolls and not the other land a thousand times or 3600 times off, and the answer still looks like a number.