- #1
Master1022
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Homework Statement
I am trying to figure out how an inductor works in depth. It should be something very simple to find, but I have yet to find an explanation that goes through the process step-by-step in a non-circular way.
I can solve the inductor differential equations and do phasor analysis with inductors with little problem (I know AC is different), but have always struggled to gain a solid intuition.
My current thoughts:
(assume we have a DC voltage connected to an LR circuit)
This is what I think happens:
1. The voltage applied causes a rate of change of current as [itex] V_{app} = L \frac{di}{dt} [/itex]
2. As the current increases, there will be a back emf created that opposes the applied voltage
3. Therefore, the applied voltage decreases and thus the rate of change of current decreases
This is where I cannot reconcile the beginning and end of the process as searches seem to suggest that the back-emf is proportional to the rate of change of current (as predicted by Lenz's law)
It would make sense if the back-emf was proportional to the current because:
- as the current increased, the back-emf increased
- voltage applied decreased and rate of change of current approaches 0
(much like a terminal velocity diagram), but I don't think this would lead me to the correct value of the final current
However, if it is proportional to the rate of change of current [itex] V_{back} = k \frac{di}{dt} [/itex] , I have problems understanding how the charging graph can arise.
Here are the two cases I can think of to do with the proportionality constant (ignored case where constant > L):
1. constant = L
- therefore, it would create a back-emf equal to the DC voltage, and thus the rate of change of current would = 0
- then would continually happen as the back-emf oscillates between said value and 0
2. constant < L
- doesn't really make the DC applied voltage would remain the same, but the applied voltage would never match the DC voltage and rate of change of current would always be greater than 0
I would appreciate any help in explaining which (if any) of the above explanations are correct and clarifying/correcting any wrong points I have made.
Thanks in advance.