apparent inductance vs. incremental inductance

CheyenneXia

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.

Antiphon

Use the incremental when there are small changes in the current or applied voltage and you are interested what happens because of it.

CheyenneXia

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

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

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?

sophiecentaur

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.