Apparent inductance vs. incremental inductance

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Discussion Overview

The discussion revolves around the concepts of apparent inductance and incremental inductance, particularly in the context of their definitions, applications, and differences. Participants explore when to use each type of inductance, especially in relation to linear and non-linear systems.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants define apparent inductance as the ratio of magnetic flux (Phi) to current (I), while incremental inductance is defined as the derivative of magnetic flux with respect to current (dPhi/dI).
  • One participant suggests using incremental inductance for small changes in current or voltage, while apparent inductance may be more appropriate for larger changes.
  • Another participant questions whether incremental inductance should always equal apparent inductance in linear scenarios, expressing confusion about the necessity of distinguishing between the two.
  • A participant provides an example involving an arc lamp, explaining that incremental inductance can be negative, which can lead to dangerous situations without proper components like a ballast.
  • There is a discussion about the relationship between apparent and incremental inductance, with one participant likening apparent inductance to DC current and incremental inductance to small AC fluctuations superimposed on it.
  • Another participant challenges the idea that total inductance can simply be the sum of apparent and incremental inductance, emphasizing that non-linear devices introduce distortions that complicate this relationship.

Areas of Agreement / Disagreement

Participants express varying views on the definitions and applications of apparent and incremental inductance, with no consensus reached on when to use each or how they relate to one another in non-linear systems.

Contextual Notes

Participants highlight the non-linearity of the Phi vs. I curve as a key factor in understanding the differences between apparent and incremental inductance, but do not resolve the implications of this non-linearity on practical applications.

CheyenneXia
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I only know that apparent inductance = Phi/I, incremental inductance = dPhi/dI.

Two definitions because of the non-linearity of Phi vs. I curve.

So is there anyone who can tell me when I should use incremental inductance and when apparent inductance?

Many thanks.
 
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Use the incremental when there are small changes in the current or applied voltage and you are interested what happens because of it.
 
So does it mean small changes in current, incremental. Big changes, apparent.

I guess if phi vs. current is linear, incremental should be equal to apparent. Then why not incremental all the time?

Thanks.

Antiphon said:
Use the incremental when there are small changes in the current or applied voltage and you are interested what happens because of it.
 
The incremental can be very different.

In fact it can actually be negative. An arc lamp is like this. For example a lamp might have 100 Volts and 1 Amp flowing through it. So if it were a resistor it would have an apparent and incremental resistance of 100 Ohms. This is an incandescent light bulb.

Have you ever wondered why a fluorescent lamp needs a ballast? A fluorescent lamp might also be made to operate at 100 Volts and 1 Amp. But it would explode without a ballast while the incandescent lamp doesn't need it.

The answer is because the fluorescent lamp has a 100 Ohm apparent resistance and perhaps a -50 Ohm incremental resistance.

Imagine what that means if the lamp flickers for a second and draws a bit more than 1 amp. It's total resistance will decrease making it draw yet more current. It will in fact run away and explode. The ballast provides positive incremental impedance so that the sum of lamp and ballast incremental resistance is never negative.
 
Hey, I think I get it. Apparent inductance is like DC current while incremental inductance is like the small fluctuating AC current superimposed on the DC current. Am I right?

So the total inductance should be apparent+incremental?


Antiphon said:
The incremental can be very different.

In fact it can actually be negative. An arc lamp is like this. For example a lamp might have 100 Volts and 1 Amp flowing through it. So if it were a resistor it would have an apparent and incremental resistance of 100 Ohms. This is an incandescent light bulb.

Have you ever wondered why a fluorescent lamp needs a ballast? A fluorescent lamp might also be made to operate at 100 Volts and 1 Amp. But it would explode without a ballast while the incandescent lamp doesn't need it.

The answer is because the fluorescent lamp has a 100 Ohm apparent resistance and perhaps a -50 Ohm incremental resistance.

Imagine what that means if the lamp flickers for a second and draws a bit more than 1 amp. It's total resistance will decrease making it draw yet more current. It will in fact run away and explode. The ballast provides positive incremental impedance so that the sum of lamp and ballast incremental resistance is never negative.
 
CheyenneXia said:
Hey, I think I get it. Apparent inductance is like DC current while incremental inductance is like the small fluctuating AC current superimposed on the DC current. Am I right?

So the total inductance should be apparent+incremental?

Not really. Total inductance differs from incremental inductance in the same way as the gradient of a line from a point at the bottom to the top of a mountain differs from the slope of a particular bit of the track going up.
Basically, if the incremental inductance is not the same as the 'apparent inductance' then the device is non-linear and will introduce distortions into a large signal.
 

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