Question

What is the derivative of voltage with respect to time?

Answer 1

Well, when I think of derivative with respect to time I think of something changing and when voltage is involved I think of capacitors.

A capacitor is a device that can store charge `Q` when a voltage `V` is applied. This device has caracteristics (physical, geometrical) described by a constant called capacitance `C`.

The relationship between these quantities is:
`Q(t)=C*V(t)`

If you derive with respect to time you get the current through the capacitor for a varying voltage:

`d/dtQ(t)=Cd/dtV(t)`

Where the derivative of `Q(t)` is the current, i.e.:
`i(t)=Cd/dtV(t)`
This equation tells you that when the voltage doesn’t change across the capacitor, current doesn’t flow; to have current flow, the voltage must change.

(I hope it helped)

Answer 2

This only applies to Alternating Current. It is the inverse of the sin (or cos) wave form between the peak voltages.

Explanation:

Because AC voltage varies in a sinusoidal waveform, the derivative at any point is the cosine of the value.