RC Circuit - Numerical time domain analysis

[D.A.(Tony)Stewart]

In a RC circuit, if the voltage source is a sinusoidal source, I found the given equation. C is constant.
I tried to solve this problem in time domain. So, I use a source in an EDA tool. I found the current in time. I know the voltage. I use simple numerical derivaton df(x)=[f(x2)-f(x1)]/(x2-x1). In this case, derivation is almost zero at the peak and bottom of the sinus. So, capacitance goes infinite. What am I doing wrong?
View attachment 115956

I dont see an error in result in EDA.

The peak sin voltages will always result in a zero crossing of current for any ideal reactive component. For C, current peak leads voltage peak by 90 deg and for L it lags. It will always be 90 deg phase difference for V and I in any ideal reactance. Even so with variable C changing with V or t, but not if lossy with internal series R (ESR).

 

[Ratch]

Ratch, I am looking for time domain numerical solution.

Guys, please do not try to change topic. I know phasor, I know differential equations, I know everything about the circuit theory. I do not know how to solve this problem in MATLAB in time domain. No hand-solution, no differential equation, no analysis on paper.

Is it clear enough?

It is now, but you did not specify only a MATLAB solution in your first post. I for one, do not have MATLAB or know how to use it.

Ratch

 

[BradtheRad]

I for one have not heard of a capacitor which changes in value during an AC cycle, and back again by the next cycle. (Unless it might be a varactor.) So these calculations appear to be putting the cart before the horse.

However I confess I do not know what inventions are in the works. A great many possibilities open up, if there were capacitors which can be made to change their own value, in response to a simple electrical signal.

Even more possibilities, if we could have inductors/ transformers which do the same thing.

The calculations would become a lot more complicated, but it would be worth it to have such advanced components.