Is there a qualifying exam on the road to the Ph.D.? When can I expect to graduate?

You have to take a qualifying exam in the spring of your second year (at which point you'll typically have completed all or almost all your coursework). This exam consists in an oral presentation of your Ph.D. research proposal. This is an excellent opportunity for you to get feedback on your research direction from a faculty committee. Just betweeen you and me, I have never seen anyone fail the exam - sometimes a student may be asked to take an additional course to address an apparent gap, and in rare cases a student may be asked to retake the exam. So it is really more an opportunity for the student than a selection tool for the faculty. We can afford not to be selective at the qualifying exam level because we are highly selective at the admission level. The duration of the Ph.D. is typically 5-6 years. We shoot for five.