Interviews in general are a whole can of worms. Not least because they are very culturally dependent. Not just between countries and continents, but between different "flavours" of engineering.
You need to be clear about what sort of person you want for the role, and what their abilities need to be. I have never been asked to bring a calculator to an interview, and I have never had an interview that assumed I would have one with me (my Casio CFX200 is way too valuable now to wear regularly!). I have only been asked for my CV once, which was ironically the only occasion that I didn't have one because it was at short notice and half way down the country. As a matter of course, I tend to make sure I have a ballpoint, a fine drawing pen and a mechanical pencil with me, mainly because I get a bit paranoid that one or another won't work. I wouldn't necessarily expect an engineer to carry a pen about their person anyway these days as a habit anyway. A pen would indicate a lack of preparation, but I would give no more weight to it than I would, say, to a crooked tie or less-than-shiny shoes.
What I would expect, however, is that they could give me a ballpark figure for some value or other. Your candidate should certainly have been able to give a value for your Ohm's law calculation, but they may have got flustered by something previously. Not long after graduating, I went for an interview with a set top box manufacturer near here. After reporting in, I had been sat for 15-20 minutes in a freezing entrance lobby, waiting for my interview. After a very short chat, the guy interviewing me wrote down some numbers and asked me to cross-multiply them. At that point, my brain totally forgot how to do that simple thing. I probably hadn't done it since school, and it just wouldn't come back to me. He continued to press and press and press, when it was abundantly clear that I couldn't do it. It wasn't a stress test, it had just become bullying. He didn't find out a thing about my analogue, RF or digital design ability, what I had done in the past, PCBs I had made, or anything relevant to the job. All he had found was that I couldn't cross multiply. At the age of 23 or whatever, you just sit and take it, at 33 you don't.
This probably answers one of your questions, but if an interviewer is getting anally retentive about me not having a pen or a calculator, then I really don't want to work there. I hate wastes of time so there is no point continuing the interview.
Accidental bullying happens an awful lot. Usually from engineers who are getting into what Jeri charmingly terms a pissing contest. Who can piss highest up the wall. The trouble is, you are on their ground, they choose the subject, and the chances are that they can find something that you just haven't even heard of. They are probably looking for reasons not to employ you, having already selected who they really wanted from the application CVs (Resumes). For an example of accidental bullying, see one of the engineerblogs here
http://engineerblogs.org/2011/01/interview-questions-on-transistors/ even now he doesn't realise that's what he is doing.
Had the guy without a pen arrived late, looked scruffy and given a couldnt-care-less attitude then I would have cut the interview short after 10 minutes. There is no point wasting both your and his time. Personally, I might have gone with the "tell me a bit about what you do" and then asked relevant questions, maybe steering it around to Ohm's law. One of my favourite interviews was, as Dave suggests, a populated PCB. They handed it to me and said "tell me about this". Unfortunately I did too well on that test, it was for a technicians job and I was giving engineer level answers. I guess it did the job for the employer though, which is really what it is all about.
If you want to test maths and physics, set a written 30 minute exam. If you timetable interviews correctly then it can be done as an overlap with the previous candidate. You will probably find out a little about their standard of written language, drafting and presentation skills too. This can then form the basis of the interview.
As an aside, be aware that they may not know (or at least commonly use) the same term that you do. I use Kirchoff's Current Law regularly, but because I don't need to name it, it was embedded behind all the other rubbish in my brain and I just couldn't remember what it did! Honestly! I mean, that was probably not just week 1 at uni, but day 1 of Physics at Sixth Form College. I guess that shows the value of written questions for some people. I guess I'm just getting old and the stuff I don't use is getting pushed out by new info!
Mike
Edited to add: I still use the HP-28S I got for uni, but this is resident on my iPod (also runs on iPhone etc)