Regarding the inductance model

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    Inductance Model
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Discussion Overview

The discussion revolves around the behavior of an inductor when a switch is opened in a circuit, particularly focusing on the implications of the voltage and energy relationships in inductors. Participants explore theoretical scenarios and the limitations of the inductance model, considering aspects of energy storage and circuit behavior.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that when the switch is opened, the voltage across the inductor could theoretically approach negative infinity, raising questions about the validity of the Vl = L*di/dt model.
  • Another participant corrects the voltage equation to V = -L*di/dt and emphasizes that the energy stored in the inductor is finite, represented by El = L*i^2/2.
  • A different viewpoint highlights the complexity of the problem, noting that opening the switch creates an open circuit, which complicates the analysis and may lead to undefined behavior without additional assumptions.
  • Some participants discuss the potential for a spark across the switch due to a large induced EMF when the switch is opened, suggesting that this could complicate the scenario further.
  • There is a mention of substituting the battery with a short circuit at the moment of switching off, raising questions about how this would affect the circuit dynamics and the relevance of the inductance model.
  • Clarifications are made regarding the dimensions of energy and potential in the context of the equations presented, with some participants debating the notation used for energy in the inductor.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the inductance model and the behavior of the circuit when the switch is opened. There is no consensus on whether the model has inherent flaws or how to properly define the situation without additional assumptions.

Contextual Notes

Participants acknowledge that the problem is not well-defined and may require assumptions about capacitance or circuit behavior to be solvable. The discussion also touches on the limitations of the inductance model under certain conditions.

MechatronO
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The inductor below is conducting an arbitrary current, with the switch on.

rlcircuit.gif


Suddenly the switch is set off and and voltage over the inductor raises to the negative infinity according to

Vl = L*di/dt

However, voltage is defined as energy per charge.

V=J/C
The energy stored "in" the inductor is finit and

El = L*i^2/2

Combining these equations, would the voltage instead then raise to

Vl = L*i^2/(2*C) ?

Where C is the sum of all free charges or something, relevant for the equation?

I guess what I've wrote above is far to simplified to describe what would happen, but let's consider this thought experiment also.

Imagine that there are only two relevant charges in the whole system. When the current is switched off, this would get an infinite potential energy distributed on a finite number of charge.
This would thus have inifinite energy created out of a finite amount of energy, thus the Vl=Ldi/dt model must begin to show serious flaws at some point?

EDIT: And no we don't consider things such as parasitic capacitance, eddy current or anything like that here.
 
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MechatronO said:
Vl = L*di/dt
Should be: V = -L*di/dt

The energy stored "in" the inductor is finit and

El = L*i^2/2
Should be: Energy = L*i^2/2

EI does not have units of energy.

Combining these equations,
 
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The problem with this problem is that it is not well defined or very complicated to solve. Just opening the switch gives you a situation of an open circuit, and you don't know what happens. You can treat the opened switch as a capacitor with some assumed capacitance to make the problem well defined. It could of course get worse and you have a spark across the opened switch, because in the very first moment a very large EMF is induced in the circuit.

Another possibility is to switch such that the battery is substituted by a shorc-circuit at the moment you switch and then kept. Imho that would make the most sensible question and a good exercise in integrating quasistationary initial-value problems in circuit theory.
 
NascentOxygen: Ei sure does have the dimension energy.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indeng.html

vanhees71: Let's assume no capacitance at all and that the voltage could reach to infinity therefore.

Why would changing the battey to a short circuit at the moment of switching off change the situation?

The point of all this is not really to study a practical circuit, but just a curiosity to see wether the Ldi/dt model has a shortcoming or non defined result, as ohm's model (law) has when R reaches zero in

I = U/R
 
MechatronO said:
NascentOxygen: Ei sure does have the dimension energy.
If E is potential and I is current, EI does not have units of energy.
 
Aha, you see i in El i just the letter E with a badly implemented subscript L, representing energy in the inductor L. EL would be better, as I even myself confused i with L in the last post.
 

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