For a embedded systems designer (who should know both analog and digital):
Question: we have several analog signals coming in to an analog MUX, and considering the signal paths and the MUX itself, the effective signal impedance at the output of the MUX is 1kohms. We need to acquire the MUX output with a 10-bit A to D. The input to the sample-and-hold has capacitance of 100pF. What is the fastest sample rate to ensure accuracy of better than 1/2 lsb?
I've had answers like "oh, that's easy, that's just the Nyquist rate, twice the frequency of highest frequency the signal contains", or "There's no limit, just whatever speed the AD can handle".
The right answer can be obtained without a calculator or even pencil and paper.
Then ask them to draw a typical A/D front end, showing analog signals, analog MUX, S+H, A/D, showing how they would connect the analog ground, and digital grounds to the MUX select pins, and ask what effect there would be if some of the current going to the MUX select pins also flowed in part of the analog gnd... the fun really starts then...!
What about this one:
You like milk and sugar in your coffee.
Should you put milk in your coffee before stirring or after stirring if you want to have the hottest drink?
This system can be described by overwhelming equations but a simple knowledge about heat transfer should be all you need to answer...
Suggestion for a power engineer:
Draw a standard simple single-phase rectifier bridge comprised of a 4-diode bridge and DC capacitor. The AC feed to this is (lethal) mains supply, and the DC load is a resistor, the capacitor is sized such that voltage ripple is small. Ask them to draw waveforms in correct time relation of: AC voltage, current in the AC lines, current in the capacitor, voltage and current in the load resistor, and voltage and current for ONE diode.
Then tell them: OK, now you have this set-up operating on your test-bench, and you want to look at the voltage across the load resistor. The test bench has a standard scope - show how you would set up the test bench to do this. (You could say "mains-powered scope" but that could be giving too much away, best to see if they ask for clarification first - better yet, prepare the drawing showing a scope with a mains lead attached.)
You would be amazed at how many power engineers think that it is OK to connect the earth of the scope probe directly to the negative output of said rectifier, without considering whether either the rectifier or the scope should be powered from a mains isolation transformer.
Then if they do mention "oh, you need a mains isolation transformer" the next question is: OK, the test bench has one of those; now where is the best (safest) place to put it, on the supply to the rectifier or the scope?"
For those that know their stuff, there is only one answer... and it could mean the difference between life and death....
I once read an article about how to make a set of cufflinks from a pair of old blown 2N3055 transistors. The object being that anyone who recognised them would probably start a conversation. But then how many new engineers would know the 2N3055 these days? (And how many would wear cufflinks??)
That's the challenge: to find a question that just about any EE would know the answer to--but fakers wouldn't!
I once read a mystery story--don't remember by whom--where the detective figured out the nature of the murderer by a crossword puzzle partially filled in that he left-behind; the detective figured out that the murderer "hung around" with chess players but did not actually play, because he filled in an item about way the game is played, but not one related to board set-up: that the white square is positioned to the right-hand corner of the board--which is something every player knows, but is never spoken about, no need to.