This is one of the cases that Larson often points out, where the math is correct, but the concept is wrong.Horace wrote: ↑Mon Jun 25, 2018 6:44 pmIn EE you'd have +20 ohms of inductive reactance, -20 ohms of capacitive reactance and XL + XC = 0.
It is worth noting that capacitive reactance is always negative and inductive reactance is always positive. Both refer to the imaginary part of the impedance. The real part of the impedance is the resistance.
Both resistance and reactance are measured in ohms, which is conceptually, "mass per unit time". So look at a "mass" analogy--if I have a kilogram of mass and a kilogram of negative mass, then drop them both on the same side of a scale--the scale reads ZERO--but there are still 2 kg of "mass" sitting on the scale--the mass does not disappear into a puff of logic.
This is what I have found is happening with resonance. The scale may read zero, but there are still two reactances present, that form the magnitude of a vector in the next, scalar dimension as: sqrt(XL^2 + XC^2) = 28.3Ω, given the 20Ω example. If you notice, that does not come out to zero. (It is actually a little more complicated than that, as you have to account for phase angles, not just 90°, but serves to illustrate the idea.)
BTW, the whole concept of reactance and impedance is misleading, as they are trying to express an angular velocity (reactance) as an axial, linear one. Reactance is the angular version of resistance, which is why it looks the same, but acts differently. (I now use the "reciprocal" concepts of jωL and 1/jωC.)