# I need help understanding inductive reactance

1. Mar 4, 2013

### rp8308

Hi guys,

I have a small pet project at the moment and I'm trying to look at eddy current losses in transformers.

Whilst researching my project I realised that my AC current, when applied to the coil (wrapped around the steel core), would be subject to an inductive reactance. Is it correct in believing that my intrinsic inductance L = NBA/I would then change because the applied current is constantly changing?

How would I observe how my inductance changing with time? I assumed it would be something along the lines of taking I = I0sin(wt) and therefore L = NBA/I0sin(wt)

My physics is rusty and my power electronics is non evident, so if someone could clear up my misconceptions it would be great.

2. Mar 4, 2013

### rp8308

So if the induced EMF in the coil, that opposes the changes in current (Lenz's law) is

ε = - L dI/dt

then if I = I0sin(wt)

then dI/dt = I0 w cos(wt) = wI

therefore L = ε / (wI) = ε / (w I0 cos(wt))

This gives me the changing inductance with time?

I will also add a paragraph of context to help. So I have an AC current of about 100 amps applied at a frequency of around 100Hz. I have a coil producing a 2 Tesla field for 2-3 seconds. The coil is wrapped around a steel core which will then experience heavy eddy current losses (I am actually investigating eddy current losses). I am looking to have an inductance of about 2mH. But I am no worried that this inductance changes with my alternating current. I want to see how the inductance is changed over time!

3. Mar 4, 2013

### Hassan2

Hi rp8308,

Assuming a linear core, the inductance is independent of the current ( and time). Please review the definition of the inductance.

To investigate (calculate) the eddy current loss, You need to find the eddy current distribution in the core ( the eddy current in the coil is usually negligible) and this is not going to be easy unless you resort to a numerical software.

4. Mar 4, 2013

### rp8308

Ok thanks.

But surely for ferromagnetic materials the permeability of the core will change with the applied magnetic flux (changing current)? Won't this affect the inductance of the coil?

5. Mar 4, 2013

### Hassan2

Yes, for high flux densities, e.g. larger than 1 Tesla, the non-linearity of the core can not be neglected and the inductance becomes dependent of the flux density(hence on the current). In this case, defining an inductance for the circuit is not going to be helpful. Nonlinear magnetic field analysis is only possible via numerical methods such as finite element method. Furthermore, if the core is not laminated, for relatively high frequencies, the flux concentrates near the the outer surfaces of the conductor causing the flux skin effect even with a linear core. Again a numerical software can take care of this.

6. Mar 4, 2013

### rp8308

ok, many thanks Hassan. I had been hoping for a way to make some estimations from first principles but I will now look into finite element analysis. I have a program called FEMM 4.2 I will work with.