I'm taking an electronics course to get a physics minor (I'm an applied math major) and today, the professor shows a diagram of an ideal current source connected to an ideal inductor. Crazy stuff I know.
The problem I'm having is that the book and his lecture notes do not treat the independent current source as an actual independent current source. That is, the current is a function with respect to time t, rather than some numerical value like 1A. Hence it is a dependent current source. (Obviously this was done to make the problem easy and/or solvable.)
Despite the lack of care given for using the appropriate symbols, it made me wonder what the actual response would be for an ideal independent current source connected to an ideal inductor. I am a math major after all.
It's been a semester or two since I took ODEs and PDEs, so my differential equations are a bit fuzzy. But I have a feeling that a Heaviside step function and Laplace transforms are not going to work here.
I would argue that the voltage across the inductor would be indeterminate at the edge of the current step and zero after that. Essentially a discontinuous function that approaches infinity at t=0 and then 0 for t>0.
Obviously this isn't physically realizable, but I was curious how one would go about solving this even if the solution diverges.
So my question. How would you attempt to solve this problem? Heaviside step function and Laplace transform or some other method? Also, what change is needed to make this problem solvable? For instance, would a parallel resistor of some finite value do the trick (so you could convert to a Thevenin equivalent circuit)?