The Electrician
Active Member
Only the OP could answer that, my guess is that the first is wanted. The second could only be an academic/mathematical derivation with in my opinion little practical value and too little information to begin. In other words OP has to do that himself.
Even though this was posted in the general chat forum and not the homework help forum, it seemed to me to have the flavor of a homework problem; this would account for the second case seeming to be an academic derivation. Even Mr. Al apparently thinks it's homework; he says, "...it often depends on the course and where they are in that course..."
Hi again,
Yes it could be a trick question aimed at misleading the student into thinking that he has to use the entire circuit to calculate the 'resonant' frequency and that somehow it might be needed while it's a much simpler question.
Because the circuit as is contains two independent circuits, the resonance of the first has nothing to do with the current in the second.
I would have thought that if they wanted us to do the entire circuit then they would have specified at least some small generator resistance, but then again it often depends on the course and where they are in that course.
For example, if they were trying to exemplify how perfect sources do not have any series resistance then the circuit is to be analyzed as is, but on the other hand if they were trying to point out how most real life sources have at least some series resistance no matter how tiny, then we have to analyze the entire circuit to get the true solution. It depends a lot on what they were talking about in the course just prior to asking this question.
Interestingly, as a third possibility they might be handed a schematic from a real life device and asked whether or not the series resistance of the generator matters in that circuit...then it would be up to us to do a few calculations and decide.
Whether or not the source has some resistance, the addition of Cp changes things. Furthermore, if Cp is not present, then the resonance frequency is the same whether you define it to be the frequency of maximum current from the source, or the frequency of zero phase angle of the source excitation.
When Cp is present, those two definitions give different frequencies. To see that this is true, I picked some arbitrary component values:
Lm = .1
Rm = 10
Cm = 1 µF
Cp = 5 µF
Then I plotted the phase angle and and magnitude of the current from the source, with an assumed voltage of 1 volt, and an internal impedance of zero. I've attached a couple of images showing the results. The phase angle is shown in red and the current magnitude in blue. I've subtracted an offset from the current magnitude so it will appear near the x-axis.
In the first plot the Cp capacitor is absent; the frequency of maximum current magnitude is the same as the frequency of zero phase angle. Either criterion will give the same resonance frequency.
In the second plot, the Cp capacitor is present. It can be seen that the frequency of zero phase angle increased, and the frequency of maximum current decreased. The resonance frequency is not the same for the two criteria, and neither is the same as the resonance frequency of the series Lm-Rm-Cm circuit alone.
There are three possible resonance frequencies that could be associated with the complete circuit, even when the source impedance is zero.