Let’s start with the familiar expression for Ohm’s law:
V = I R [1]
For AC circuits, we generalize this to
V = I Z [2]
where Z represent the complex impedance. Let’s focus on the case where Z = 1/iωC for a capacitor.
Another quantity of interest is the dissipated power:
P = V^2 / R [3]
The problem is, in the last two equations the symbol “V” is being used with two different,
inconsistent meanings. In equation [2] V must be interpreted as a complex number i.e. a
phasor. In equation [3] V must be interpreted as the actual, real voltage. Interestingly
enough, in equation [1], either interpretation is correct.
So the question is, what if any better notation is available. I know that "sometimes"
people write little hats over the phasors, but that is a bit cumbersome, and after
about the first five minutes they drop the hats.
The way I see it, you always need to understand what an equation means
before you can use it. Inconsistent or ambiguous notation makes this
slightly harder, but only slightly. So one option is to just live with
it. OTOH if anybody has any suggestions for how to do things better, I
would definitely like to hear about it.