How to calculate the voltage drop in this case?
Interestingly enough, this is a question asked on interviews as well! So if you're a student, definitely pay attention to these problems. They will come in handy when applying for a job or an internship.
That being said, I don't have a lot of time at the moment to solve the problem (maybe I'll do it later), but I'll point you in the right direction. Always simplify your problem and don't get intimidated voltage sources with non-dc components. At the end of the day if we forget the sine function of the supply and we just call it V1, then your simplified circuit looks like this:

Then the problem is simplified by KCL. We know that the voltage Vx is nothing more than Ix*R. So applying KCL we have that I0+I1=Ix+X2.