Is there an English equivalent for the German jawohl?

I do some online tutoring in math. We are told not to do homework for the students but to work with them, breaking the problem down and asking questions in a Socratic dialog. I therefore frequently find myself answering yes to the answers given to my questions.

The problem with yes in this context is that the word can come across as curt and cold. Words for yes in other languages tend to have the same problem. Si and da are not any better, though oui at least has a bit of a lilt. The German jawohl seems perfectly suited. It is yes with enthusiasm. If there were an English equivalent, I would definitely make use of it, though not exclusively, since that could get a bit tiresome.

To inject some more emphasis, I never just say yes. I will say things like Yes!, Yes, good!, Yes, very good!, Excellent!, That’s it! or sometimes Yup!, depending on the situation. I am not completely comfortable with any of these, because they seem a bit forced. Any suggestions for variations? Could we use a new word?