# Measuring time constant using an inductor with a core vs. no core

• Taulant Sholla
In summary, inserting a steel (or iron) core into an air core coil results in much different experimental results than predicted. If using a gapless structure, the inductance is mostly affected by the air gap and less sensitive to the permeability of the core.
Taulant Sholla
I'm doing a simple RL Circuit Lab where students use 800- and 1600-turn air core coils to measure the time constant. Experimental results very nicely agree with predicted results.

However, when students insert a steel (or iron) core in the coils, experimental results are far different than predictions.

Any ideas are appreciated!

The inductance of your air coils is maybe in the millihenry range, and I am guessing you may be using short time constants of a fraction of a second. These short time constants involve rapid rate-of-change of flux, which might create large eddy current losses in the core.

Yes, inductance ranges from 10-40 mH, with time constants in the realm of 0.6-0.8 milliseconds. I had no idea these losses are so substantial!

Thank you.

Taulant Sholla said:
Yes, inductance ranges from 10-40 mH, with time constants in the realm of 0.6-0.8 milliseconds.
What time constant do you get with the core inserted?
From that, compute the value of coil inductance when the core is inserted.

Maybe inserting a ferrite rod would give a result for the pupils and would not involve eddy current problems.

I think the question is whether the increase if inductance due to a core, would slow the response to the point where there is enough core to handle the flux.

What type of core are you using? What is the geometry?

If it is a gapless structure, then you may see large variations in the inductance because of the unintended introduction of an air gap due to misalignment, surface roughness, or contamination. A tiny air gap can have a really large effect. If this is the case, I would suggest including an intentional air gap, like some paper or plastic. With a gapped structure and a high permeability material, the inductance is mostly affected by the air gap and less sensitive to the permeability of the core. There is a really significant difference between a 1mm ± 0.1mm gap and a 0.1mm ± 0.1mm gap.

I have tried making simple transformers wound on a steel bolt and they do not work at all!

DaveE said:
What type of core are you using? What is the geometry?

If it is a gapless structure, then you may see large variations in the inductance because of the unintended introduction of an air gap due to misalignment, surface roughness, or contamination. A tiny air gap can have a really large effect. If this is the case, I would suggest including an intentional air gap, like some paper or plastic. With a gapped structure and a high permeability material, the inductance is mostly affected by the air gap and less sensitive to the permeability of the core. There is a really significant difference between a 1mm ± 0.1mm gap and a 0.1mm ± 0.1mm gap.

I've included an image of the coil and core we use below. For our RL lab, we simply use one coil, not the two as shown. Using a single 800-turn coil with the pictured closed loop core increases the inductance from about 10mH to 70mH. Not exactly sure what you're suggesting--basically shimming remaining air gaps with additional high permeability material?? Again, our results with no core whatsoever are great; with a core, whether a single bar (removed from the loop), or the entire closed loop--not even close.

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Baluncore said:
I think the question is whether the increase if inductance due to a core, would slow the response to the point where there is enough core to handle the flux.
I was thinking a greater time constant might yield better results between experiment and prediction. We do indeed get good results now using 800- and 1600-turn air core coils. Using any kind of core (laminated closed loop square core or laminated single-bar core) yields very inaccurate results. So for now I just skip using cores, but it would be great if students used the core, measured the much greater inductance, and still got good agreement between experiment and prediction. This is not the case.

Baluncore said:
What time constant do you get with the core inserted?
From that, compute the value of coil inductance when the core is inserted.
This is a possibility, but right now students use an LCR meter to measure inductance and resistance, and use this as the basis for comparing experimental results to predictions. I like having them get hands-on experience with LCR meters and others devices as mush as possible.

Taulant Sholla said:
Not exactly sure what you're suggesting--basically shimming remaining air gaps with additional high permeability material?
No, make an air gap between the core halves (assuming there was none originally); a part of the path the magnetic flux must travel that doesn't go through the high permeability core material. This makes the total permeability of the structure more stable. You will, of course, get less inductance than with no gap, but it will be harder to saturate the core and the assembly will be less sensitive to "accidental" air gaps. The material you put in the gap between the core haves can be anything non-magnetic, like post-it notes for example.

How are they measuring the time constant? What is your excitation and how do you observe the decay?

DaveE said:
No, make an air gap between the core halves (assuming there was none originally); a part of the path the magnetic flux must travel that doesn't go through the high permeability core material. This makes the total permeability of the structure more stable. You will, of course, get less inductance than with no gap, but it will be harder to saturate the core and the assembly will be less sensitive to "accidental" air gaps. The material you put in the gap between the core haves can be anything non-magnetic, like post-it notes for example.

I'll try this - thank you. Learning a lot here.

DaveE said:
How are they measuring the time constant? What is your excitation and how do you observe the decay?
They use an integrated lab management setup from PASCO. A single interface box provides signal generator output and inputs for various sensors. We can adjust several AC parameters, and can also specify sample rates for voltage and current sensors. We gather a graph like this (except we collect voltage rather than current data). This experimental results is compared to tau=L/R where L and R are measured using an LCR meter.

Taulant Sholla said:
This experimental results is compared to tau=L/R where L and R are measured using an LCR meter.
Once a magnetic core becomes involved there are frequency effects and magnetic energy storage non-linearities such as hysteresis. That may make RL unipolar current experiments confusing.

The frequency of measurement used by the LCR meter will become more important in the presence of a magnetic core. What frequency is used for the inductance measurements? What is the make and model of the LCR meter?

Taulant Sholla said:
A single interface box provides signal generator output and inputs for various sensors. We can adjust several AC parameters, and can also specify sample rates for voltage and current sensors. We gather a graph like this (except we collect voltage rather than current data).
OK, so you are looking at the voltage step response of an L-R low pass filter?

Baluncore said:
Once a magnetic core becomes involved there are frequency effects and magnetic energy storage non-linearities such as hysteresis. That may make RL unipolar current experiments confusing.

The frequency of measurement used by the LCR meter will become more important in the presence of a magnetic core. What frequency is used for the inductance measurements? What is the make and model of the LCR meter?
Thanks for your continued help! I'm traveling and have limited connectivity opportunities, hence the gaps between my responses. Here's the LCR meter we use:

"Proster LCR Meter Capacitance Inductance Resistance Tester Multimeter Self-discharge with Overrange Display"

DaveE said:
OK, so you are looking at the voltage step response of an L-R low pass filter?
Yes, students measure the experimental time constant and compare to the predicted value (based on LCR values given by an LCR meter) for a series of RL combinations based on 800- and 1600-turn coils and 5-,10- and 22-ohm resistors.

## 1. What is the purpose of using an inductor with a core in measuring time constant?

The core in an inductor serves to increase the inductance of the circuit, which affects the time constant. By using a core, the time constant can be measured more accurately and with greater precision.

## 2. How does the presence or absence of a core affect the time constant measurement?

Without a core, the inductance of the circuit is lower, resulting in a shorter time constant. This is because the core helps to store more energy in the inductor, increasing its inductance and therefore the time constant.

## 3. Can an inductor with a core and one without a core be used interchangeably in measuring time constant?

No, an inductor with a core and one without a core will have different inductance values, which will affect the time constant measurement. It is important to use the appropriate type of inductor for accurate results.

## 4. Are there any other factors that can affect the time constant measurement besides the presence or absence of a core?

Yes, other factors such as the material of the core, the size and shape of the inductor, and the frequency of the circuit can also affect the time constant measurement. These should be taken into consideration when conducting experiments.

## 5. How can the time constant be calculated using an inductor with a core?

The time constant can be calculated by dividing the inductance of the circuit by the resistance. However, the inductance of the circuit will need to be adjusted to account for the presence of the core. This can be done by subtracting the inductance of the core from the total inductance measurement.

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