# Why does the resistance of an inductor increase when an iron core is introduced?

• Kal_Electri
In summary, the introduction of an iron core in an air cored inductor results in a considerable increase in resistance. This is due to the iron core inducing eddy currents that oppose the primary field and cause energy losses. This increase in resistance is more noticeable at higher frequencies due to the skin effect. Additionally, the core losses in the iron core also contribute to an increase in resistance. Overall, the presence of an iron core in an inductor results in an increase in impedance and a decrease in efficiency.
Kal_Electri
The inductor is initially an air cored one.When the Iron core is introduced,the resistance is found to increase considerably.Please explain.

Resistance represents power losses; I e., Z(ω) = R + jωL. It is a real component of the inductor impedance.

An iron core can have both eddy current (skin effect) and magnetic loop hysteresis losses.

Assuming you are referring to Impedance and not Resistance, when the core is introduced, the varying magnetic field of the inductor induces eddy currents in the iron core. These eddy's have their own field which opposes the primary (inductor's) field, therefore increasing the impedance.

Why is the resistance which is the real part increase?

yungman said:
Why is the resistance which is the real part increase?
Losses.

Like how? When you measure at DC, it is only the resistance of the wire and is constant no matter what. How is the induction of core change the DC resistance?

yungman said:
Like how? When you measure at DC, it is only the resistance of the wire and is constant no matter what. How is the induction of core change the DC resistance?
DC? DC hasn't been mentioned.

DC resistance doesn't change.
But if you measure AC impedance and phase angle and do a polar to rectangular calc you get a real component that is different from what a DC ohm-meter would report.

That's because the core losses are energy losses which can only show up as resistance.
And they're only present when excitation is AC.

jim hardy said:
DC resistance doesn't change.
But if you measure AC impedance and phase angle and do a polar to rectangular calc you get a real component that is different from what a DC ohm-meter would report.

That's because the core losses are energy losses which can only show up as resistance.
And they're only present when excitation is AC.

Yes exactly, sounds like the OP is confusing resistance and impedance and said resistance instead of the other

Cheers
Dave

NascentOxygen said:
DC? DC hasn't been mentioned.

DC was inferred as the OP spoke of resistance, not impedance

D

AC was inferred because the OP spoke of inductor, not solenoid.

I don't know whether he meant impedance or resistance,, but to notice a core he had to use AC.

It's an interesting experiment. One should try diverse measurements for they always turn up some unexpected jewel of insight.

AC resistance and inductance are both affected by temperature of core which at first is strange,
because there's no temperature term in either L= N$\Phi$/I or $\Phi$=μNIA/$\iota$ength

It's the core's resistivity affecting eddy currents which both cancel flux and absorb energy.
Inductance will go up slightly with core temperature because eddy currents go down..
For Resistance you have competing effects between iron core and copper windings - i don't know which way it will go.

It's most noticeable in un-laminated cores as were used in early PWR control rod position sensors.

old jim

Poor old OP.
I bet he's scuttled off with his tail between his legs. It was his first post, too!

Come back and tell us what you meant, Kal_Electri. You will get an answer once we really know what your question is.

NascentOxygen said:
DC? DC hasn't been mentioned.

But R is the DC value only! Or are you implying the skin effect cause the R to go up and this has nothing to do with the inductance. It is pure resistance that increase with frequency! That actually makes sense! I think I answer my own question!

Yungman - check my thinking

Iron losses in the core come out as heat so must cause an in-phase component of current. Else there'd be no net electrical energy transfer into core. P=VICos(Theta) and theta can't be 90 degrees if there's any watts heating the core.

So they will appear to be another resistance in parallel
which will show up as series in theveniin equivalent

and the DC ohms will differ from the ohms in real component of complex Z.

am i on track?

old jim

Skin effect and core loss are two different sources of additional Resistance. They can both be embarassing and will add to the DC resistance effect or even dominate.

What Sophie and Bob S said.

yungman said:
But R is the DC value only! Or are you implying the skin effect cause the R to go up and this has nothing to do with the inductance. It is pure resistance that increase with frequency! That actually makes sense! I think I answer my own question!
The theory of eddy current losses in transformer laminations is given in http://www.elect.mrt.ac.lk/EE201_em_theory.pdf
Page 7 shows that it increases as the square of frequency.

jim hardy said:
Yungman - check my thinking

Iron losses in the core come out as heat so must cause an in-phase component of current. Else there'd be no net electrical energy transfer into core. P=VICos(Theta) and theta can't be 90 degrees if there's any watts heating the core.

So they will appear to be another resistance in parallel
which will show up as series in theveniin equivalent

and the DC ohms will differ from the ohms in real component of complex Z.

am i on track?

old jim

I have no idea, till yesterday, the DC resistance was the only thing I consider. I am learning.

To say very simply and plainly... The Iron has drift current (because of Earth's temperature) more than air. So, naturally more magnetic flux into it causes more aligned electrons with respect to the magnetic field applied. Magnetic flux is induced into it because inductor has twisted loops (Remember Biot-Sarvat Law which explains about the motion of electrons in a circular loop). Oriented electrons, formed in this manner, are always in a way that they oppose the flow of current through it - This is the basic principle of the inductor. Now as the no of electrons increase the total opposing flux through it increases (Self- induction) and so more opposition force followed by more impedance.

Remarkably when you place a similar coil near the same inductive coil, the same voltage is generated in it, which we call as a transformer. A transformer doesn't work in very low voltages just like an inductor, because the thermally drifted electrons are absent. This is as simple as that. Make it more generalized than specialized.

Hope you get it... :)

Last edited:
jim hardy said:
Yungman - check my thinking

Iron losses in the core come out as heat so must cause an in-phase component of current. Else there'd be no net electrical energy transfer into core. P=VICos(Theta) and theta can't be 90 degrees if there's any watts heating the core.

So they will appear to be another resistance in parallel
which will show up as series in theveniin equivalent

and the DC ohms will differ from the ohms in real component of complex Z.

am i on track?

old jim

I would agree that in order for heat to be generated the current would have to be in phase with the voltage. Would we look at this as a parallel resistance or a series one?

It seems to me intuitive to call it parallel with a lossless inductor but that's just my mental laziness tying to keep it simple . Magnetizing and loss currents would simply add at 90deg.

But it could also be considered in series with an inductor of finite inductance

One could make thevenin and norton equivalents for the transformer that would help visualize.

To my tired old brain the polar to rectangular conversion of Z is the doorway to picturing it.
Admittances in parallel add. I think of losses as an admittance that absorbs power. Picturing it that way it's easier for me to arrive at the formulas, but some people are gifted with a different thought path - they can start with the formula and arrive at the picture..

When i can work something both directions is when i begin to feel confident about it.
I had trouble with magnetics because my first course was taught in English units, gilberts et al,
next one in CGS units, after that i picked up SI on my own. With my bad memory for names i still get confused.
Repeat of a post someplace else - Jack M Janicke's book "Magnetic Measurements Handbook" is a great reference for the home experimenter. I built one of his fluxgate magnetometers.

Averagesupernova said:
I would agree that in order for heat to be generated the current would have to be in phase with the voltage. Would we look at this as a parallel resistance or a series one?

in that (admittedly simplified) image, I think Rc are the core losses and Rp/Rs are the coil losses (DC resistance ofthe wire). its easy to see that its in parallel when you realize that its caused by the voltage rather than the current, as is the magnetising current (Xm).

not only does the value of Rc vary with frequency but also with amplitude for an iron core, once you start getting close to saturation.

Thanks EOW... that picture works perfectly for me and from it the formulas come naturally.

Rc also varies with temperature because resistivity of iron affects eddy currents.
But in a well laminated core they are small.

One good picture is worth soooo many words !

## 1. Why does the resistance of an inductor increase when an iron core is introduced?

The resistance of an inductor increases when an iron core is introduced because the iron core has a higher magnetic permeability than air. This means that the magnetic field produced by the current passing through the inductor will be stronger and more concentrated, resulting in an increase in the inductance of the inductor. This increase in inductance leads to a higher opposition to changes in current, resulting in an increase in resistance.

## 2. How does the introduction of an iron core affect the inductance of an inductor?

The introduction of an iron core increases the inductance of an inductor. The iron core has a higher magnetic permeability than air, which means that it can store more magnetic energy for a given current. This leads to a stronger and more concentrated magnetic field, resulting in an increase in the inductance of the inductor.

## 3. Does the size of the iron core affect the resistance of an inductor?

Yes, the size of the iron core can affect the resistance of an inductor. The larger the iron core, the more magnetic energy it can store, resulting in a stronger magnetic field and an increase in inductance. This increase in inductance leads to a higher opposition to changes in current, resulting in an increase in resistance.

## 4. Why is an iron core preferred over other materials for increasing the inductance of an inductor?

An iron core is preferred over other materials for increasing the inductance of an inductor because it has a higher magnetic permeability. This means that it can store more magnetic energy for a given current, resulting in a stronger and more concentrated magnetic field. Other materials may also increase inductance, but not to the same extent as an iron core.

## 5. Can the introduction of an iron core lead to overheating in an inductor?

Yes, the introduction of an iron core can lead to overheating in an inductor if the current passing through the inductor is too high. The iron core can cause the magnetic field to become too strong, resulting in increased resistance and heat generation. This can be prevented by using an iron core with appropriate dimensions and by limiting the current passing through the inductor.

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