When you suddenly apply 12V to the coil the resulting magnetic flux generates a back voltage equal to 12V (not 11.9V or any lesser value)
This is entirely UNTRUE.
How can a coil produce a magnetic flux if the opposing voltage is 12v ???? ?????????????????????
Hi,
This is another one of those very very good points to bring up. I like to see things like this come up because in theory we often overlook some points in order to make a more important point clear.
In this case the original statement is actually TRUE, at least in THEORY. Note we have to add the qualifier, "THEORY" because that's what we want to use most of the time in order to calculate something about a circuit. We leave the PRACTICAL for later when we feel like looking into the finer points.
We can say the statement is true in theory because of:
V=L*di/dt
and also because the flux increase follows the current increase, and thus we have from Faraday:
V=N*d(phi)/dt
where phi is the flux.
What this means is that the voltage is proportional to the time rate of change of the flux, not the absolute level of the flux itself. This is very important because that means to know the voltage we have to know the time rate of change of flux not the flux itself.
The flux is just:
phi
while the time rate of change of flux is:
d(phi)/dt
so the time rate of change of flux is the first derivative of the flux, not the flux. The flux is proportional to current in a linear inductor, so we have:
phi=K*i
Now looking again at V=L*di/dt we can solve for di/dt:
di/dt=V/L
and so with a constant voltage of 12v and an inductance of 1 Henry we have:
di/dt=12/1=12 amps per second.
Another important thing to note is that this happens even at t=0+ which is an infinitesimally short time after t=0. This means any measurable change in flux occurs immediately after t=0 in theory, so right from the start we do actually have a change in flux and therefore we actually do have a voltage.
Putting this 12 amps per second back into the original equation we have:
V=L*12
and again with L=1 Henry we have:
V=12 volts.
So this is actually a simple concept but it requires using theory rather than actual practice, and we do that often and it comes out similar to what we really see in practice, with some usually minor alterations.
The alterations we are talking about here come in the form of the parasitics like inter-winding capacitance, and of course a little series resistance. This means some current will flow immediately, limited only by the series resistance, although its path will be through the capacitances anyway not the coil turns until some very short time later. But in theory we ignore this to simplify the expressions and get something that works very similar anyway.
We talked about voltage and current near t=0 in another place at one time, and because it has been proven that the force that voltage brings about on a charge occurs without ANY delay, in theory we can say that as soon as the voltage appears the force on the charges appears simultaneously. This leads us to believe that the charge starts to move instantaneously as well, and so we can always say that the di/dt is non zero at t=0+ for a pure inductance.
As Steve nicely pointed out however, when we talk about impedance we are restricting our analysis to the AC steady state solution and ignoring transient as well as DC solutions.
I must also point out again that i think we are getting a little too deep here for the OP's liking. I believe they would do well to get a firm grasp on how resistance works first, perhaps solving a few circuits with resistances and maybe some DC voltages. This is the usual coarse of study anyway...learn DC circuits first then move on to AC circuits.