G. Mark’s Answer
Oh, absolutely. Electrical engineering is, by its very nature, applicable to a huge variety of mechanisms, applications, studies, phenomena and situations. You'll find it overlapping with mechanical engineering, chemical engineering, even petroleum engineering. And of course, EE has a close coupling with Computer Engineering. When you factor in the variety of problems those fields will be engaged to address, you can see the variety of focuses you can have in EE. My background was in Computer Science, and when I went to grad school, my school, Carnegie Mellon, did not offer a PhD in CS, but only in Computer Engineering. And it included a lot of EE, which I was definitely not versed in. As painful as it was, it was one of the best experiences I'd ever had -- pain notwithstanding. The variety of focuses I was exposed to and the brilliant people I was also exposed to served me very well in my later inventions and efforts of problem solving.
One of the things that I teach my students is the fact that approximately 70% of new innovations are due to applying principles from other seemingly-unrelated fields to the field in which the problem seems to originate. In fact, several of my earlier patents were simply "rip-offs" of applying patters from outside the field to my current problem. In one, I had been reading a book on neurophysiology, and my problem was how to make computer packet networks more resilient. Like the plasticity in the human brain that allows stroke victims to recover. Focus? Maybe not so much. And many of my earlier inventions were based on similar surprising relations.