# Varying Potential Difference for Displacement Current

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.

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)