My textbook tells me that in order to calculate the power (in watts) for an electrical circuit then the equation is $P=VI$ (volts times amps equals watts). However, I have read online that this generally only applies to DC circuits. My first question is are there any exceptions to this regarding DC circuits? Are there any components that this equation would not apply to and if so, is there an alternative?
I have also read that this same equation can be used in AC circuits providing that it is a purely resistive load and not an inductive or capacitive load. I'm assuming then that things that simply produce heat or light such as a toaster, a kettle or a light bulb would count and the P=VI equation is valid here in AC providing that the RMS values for volts and amps are used. Is this correct? If so, what are some other common appliances where this is true? In regards to capacitive or inductive loads I read that you need to account for the phase difference by adding cos of the angle to the equation. How do I find that? Or are there any ways to at least get an estimate for a particular device?
Also, my textbook says that V=IR and I have read elsewhere that this is true only in some cases but I'm having a hard time finding some straight answers as to what these special cases are. To add to the confusion, my textbook goes on to combine the $P=VI$ and the $V=IR$ equations to get $P=I^2R$ and $P=V^2/R$. It then uses these equations in examples including a hairdryer plugged into a 230 volt main socket but from my reading online, I get the impression that the $V=IR$ equation does not nessesarily work for AC circuits. If true then how can it be used in combination with the power equation and then used on an AC circuit? Also, it specifically mentions the motor in the hairdryer which I thought was an inductive device and so the simple $P=VI$ equation should not hold. So what gives? Should it not need the power factor added on too? And does the power equation hold for a DC motor if not for an AC motor? What about something like a vacuum cleaner or even a blender?
I guess what my questions boil down to is where are these various equations valid and when are they not? I want to be a able to use them at home and at work but I don't want to use them when they're not valid. Any information would be greatly appreciated.