inductors ~ mass. resists sudden change in current. so current "falls behind"
capacitors ~ springs. resists sudden change in voltage so current "gets ahead" or voltage 'falls behind"
Leading/lagging refers to the amplitude of current relative to voltage waveform. The time/magnitude relationship of the voltage waveform is more or less dictated by the PoCo.
At field technician level, I have to say the math that goes behind it is not useful.
Capacitors get installed as prescribed or according to a guideline established by OEM or engineers. Fan gets 5µF and compressor gets 30µF, based on manufacturer's specs, published guidelines or as directed by others. And as far as what techs need to know, it induces the proper amount of phase shift to produce the rotating field needed to produce starting torque in the right direction.
WestcoastApprentise has gotten a lot of grief for his post. It's unfortunate for our industry but I agree with his assessment of the techs he worked with before. Knowing 1/2 of everyone we work with is below average and doesn't care. I have said before I have known only about 10 good techs and maybe 5 great techs. The rest get by and that's it.
What I see in WCA is a very competitive person that will not allow anyone to beat him in his chosen field. Some of you that were gifted with an athletic ability know when up against another athlete that you can't let them beat you. You'll die trying.
I see WCA not able to leave something unknown. What ever it takes to solve the current question in his head he'll do it. This is potential. I know this because I've seen it before just not very often.
I don't believe in useless knowledge as there is a connectedness to be found. A person who's brain functions as a generalist finds connections where others don't.
I think WCA finds real energy in competition with his peers. A good thing for him, not so much for his peers.
Tracers work both ways.