How to write a Cover Letter for applying to a PhD program in the USA I have completed my BS and MS in physics and I want to apply at different US universities for graduate program. What I have heard from my seniors that, I should mail the program coordinator to confirm if my profile is good enough to get admitted. For that I need to write a cover letter. 


Am I in the right direction?   
Who should I contact, my potential adviser or the graduate
coordinator, to know if my profile is strong enough for getting
admitted?
Cover letter is an integral part of your application. You may look at this and this.
You could find numerous articles by simple Google search explaining Do's and Don'ts when writing a cover letter such as the above links.


  Who should I contact to know if my profile is strong?


If you are an eligible candidate according to the eligibility criteria put forward by the graduate school (usually published in the respective website), then you may contact NO ONE.
I am in Physics, now doing a PhD in France and a successful candidate in terms of International PhD admissions. I am strongly opposed to the idea of asking if your profile is good or not to a second person. It gets worse if you are going to ask this to your potential supervisor. In my opinion, it's something that you should feel withing yourself. Why do you care about Mr. X's opinions about the strength of your profile? Furthermore, if you are really motivated to work with Mr. Y then even if Mr. X tells you your profile is not strong enough, why don't you give it a try? Y will then decide if you are fit or not. I think this is a better approach than asking Y if you are strong enough to work with him.