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Capacitor V-I Charecteristics

I'm sorry but what just happened here? Can someone explain? All I know is the capacitor stuff learnt at A lvl...

cap.JPG
(edited 2 years ago)
They seem to have skimped on capital letters...?

Unparseable latex formula:

\frac{d}{dt}\left[q] \rightarrow \frac{dq}{dt}=C\frac{dV}{dt} \rightarrow I(t)=C\frac{dV}{dt}



This part was definitely covered at A-Level (right at the start when discussing the basics of capacitors, at least in AQA. Idk about OCR or the others, but I would expect it to be so.)

The next part is just working backwards, and is just an integral...

∫I(τ)dτ=∫CdV \int I(\tau)d\tau = \int CdV

where you'd throw in some boundary conditions, etc, to retrieve I(t)I(t) and V(t)V(t).

Capacitance has been assumed constant here, which for all purposes is what you should assume for any component.
(edited 2 years ago)

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