I like this question. Suppose decades of knowledge and experience and actually flawed and electricity doesn't actually work how we think it does?
Hi,
Well, for DC the equation V=R*I always holds because it is a self fulfilling definition in that if you measure V and you measure I then:
R=V/I
and that's said to be the resistance.
Then, using algebra which is perfect in itself, we rearrange to get V=R*I and it has to work because R is defined that way too.
In the AC case however, although V=R*I holds for a large number of cases (audio for example), it may not hold when the wavelength (RF) becomes comparable to one of the physical dimensions of the resistor (such as length, width, or height). In that case it has to be handled as a sort of transmission line with distributed capacitance and inductance as well as resistance where the total resistance is broken up into pieces but even then we would allow the use of V=deltaR*I which is almost the same.
So decades of theory doesnt go down the tubes, it just has to be handled a little differently sometimes. In this forum we seem to rarely talk about the applications where this would be significant however.
As to a real world application, as mentioned as the resistor heats up the resistance often goes up by some degree so we have to change it a little:
V=R(T)*I
where R(T) is the resistance function of temperature. A brief example would be:
R(T)=Ra*(1+(T-293)/1000)
where
T is the temperature in Kelvin, and
Ra is the resistance at 293 Kelvin.
This function tells us that for temperatures over 20 deg C we get a slight increase in resistance, and for temperatures less than 20 degrees C we get a slight decrease in resistance.
As the resistor heats up the temperature rises, so the resistance rises.