Hi PG,
Im not sure if you have heard of gamma correction, but your drawing needs gamma correction. Also, the size doesnt need to be that large either. I just thought i would tell you because it makes it easier to read after gamma correction and the size takes up less space.
It looks like you have the right idea but it's nicer to see the actual question the way you saw it first so i could get a better idea what is going on. I guess they just want you to solve for I(t) as shown? Didnt they give examples?
The resistance you seek is useful so you can find the time constant of the circuit. You also need to calculate the max voltage across C so i am wondering how they instructed you to do this or similar in whatever it is you are reading. The are different ways to do this so i'd have to see more of what you are reading to know exactly how they want you to do it.
In the mean time, here is a gamma corrected and resized diagram: