I have seen in alternating current that values of current and potential difference in different circuits like LR, CR or LCR circuits are found by adding them like vectors.
It also happens with amplitude of waves in wave interference.
I understand that their values varies as given in the equationI=I○sin(ωt)
but that does not make them vectors
Voltage calculation in LCR
Phasor of LCR series
Resultant Amplitude of 2 waves
Similarly net resistance or impedance to flow of current is found in LCR series as given as under. (The angle between net of capacitive and inductive reactance and resistance is 90° so cos90 becomes zero and that part is removed in formula)
The best explanation I got was that they are assumed and treated as such using phasors.
I tried to prove that the assumptions are correct by adding them as scalars(as happens in reality) but couldn't find a way.
So can you add them as scalars or atleast explain & prove what happens that makes scalar additions in reality give same answers as vector addition in assumption?
Say an LR circuit is taken