Question

16. A car battery is rated at $90\mathrm{Ah}$, meaning that it can supply a $90A$ current for $1\mathrm{h}$ before being completely discharged. If you leave your headlights on until the battery is completely dead, how much charge leaves the battery?

Short answer

The charge leaves the battery when the battery is completely dead is $324\mathrm{kC}$.

Step-by-step solution

Given information

A car battery is rated at $90\mathrm{Ah}$, meaning that it can supply a $90A$current for $1\mathrm{h}$ before being completely discharged. Then leave the headlights on until the battery is completely dead.

Explanation

A constant (hypothetical) current is supplied before the battery dies. The quantity of charge $Q$is calculated by the current $I=90A$and the time $t=1hour$.
$I=\frac{Q}{t}$

$\Rightarrow Q=It$

The time being $1\mathrm{h}=3600seconds$,

$Q=90A\times 3600sec$

$=324\mathrm{kC}$

Final answer

The charge leaves the battery is $324\mathrm{kC}$.