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Displacement current is the result time varying electric field between two plates of a capacitor and is constant when rate of change in potential difference is constant.

Now the question is whether the potential difference is increasing or decreasing with time

And my insane thoughts on this are

As $$\frac{dQ}{dt} = C\frac{dV}{dt}$$

which means as $Q$ is increases on the capacitor as time passes so does $V$. This gives out the correct answer but is confusing me. I want to know the reason behind ths. Please help me out.

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Charge changes in the same way as voltage but that doesn't mean they are always increasing or always decreasing. When you have an AC current its generally from a generator or something like that which is spinning causing sinusoidal changes in voltage so generally $V \approx sin(\theta)$ so $\frac{dV}{dt} \approx cos(\theta)$ so it changes in the same way as voltage just 90 degrees out of phase. (Basically it goes up and down)

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  • $\begingroup$ Well i don't whether it's changing in sinusoidal or exponential way but the question asks me to answer how it's varying with time with only two options increasing or decreasing ( well there are two more "0 and constant" but those are definitely wrong so never mind ). So you tell what should i tick there as sinusoidal makes both of them correct and it's a single choice question. $\endgroup$ – Augusta ASAKA Dec 9 '19 at 17:19
  • $\begingroup$ Fair enough, maybe its a question about DC, the potential difference should increase because negative charge (electrons) builds up on one side of the plate and they become less dense on the other plate (lack of electrons) so you get a higher potential difference the more the charge builds up $\endgroup$ – Stephen Jackson Dec 9 '19 at 17:24

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