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What is the meaning of the gradient of a current vs time graph?

In other words, what does the unit $As^{-1}$ or $Cs^{-2}$ represent?

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Just the "rate of change of current" very important if you are designing an electrical system but it doesn't have any particular physical meaning or it's own specific term.

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The gradient of such a graph represents change in current/change in time, which is how the current changes over time. Current is measured in Amps, (A) and time is measured in seconds (s), and therefore the units $As^{-1}$ means $\frac{A}{s}$ which is Amps per second, and represents how many amps the current changes by each second.

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