Self-inductance of an inductor - theoretical vs measurment

[Nick89]

Hi,

I did an experiment where one of the 'questions' was to determine the self-inductance of an inductor. I am going to leave out the experimental method, but if you need to know just say so and I'll try to explain.

The value I got was $$L = (3.910 \pm 0.009) \text{ mH}$$.

I am fairly confident that this is correct, because 4 people who did the experiment before me got the same value, and my teachers also confirmed that was the result we are looking for.

Now, I need to compare this value to the value obtained from the theoretical formulas.

I used the following:
$$L = \frac{N \Phi}{i}$$
$$\Phi = BA$$
$$B = \frac{\mu_0 N i }{\ell}$$

So
$$L = \frac{\mu_0 N^2 A}{\ell}$$
(N is the number of turns, A is the cross-sectional area, $$\ell$$ is the length of the inductor and i is the current.

Plugging in the values for A, l, N etc, I get a value of L = 1.79 mH.

I am about a factor 2 off..? How did this happen?

I was wondering if this could be because of the many assumptions (that may not be true here) and approximations for example for the magnetic field of an inductor (which assumes a very long inductor if i remember correctly...)?

Could that really cause such a large error? I doubt it... But if they are correct that would mean 4 people + my teacher measured the inductance wrongly?

 

[eljose79]

Hello,

Thank you for sharing your experiment and results. It is always important to compare experimental results to theoretical values to ensure accuracy and validity.

The discrepancy between your experimental value for inductance (L = 3.910 mH) and the theoretical value (L = 1.79 mH) could be due to a number of factors. As you mentioned, there may have been assumptions or approximations made in the theoretical calculations that do not hold true in your specific experiment. Additionally, there could have been errors in measurement or calculation in either the experimental or theoretical methods.

To better understand the source of the discrepancy, it would be helpful to know more about your experimental setup and methodology. Are there any potential sources of error that could have affected your measurement of inductance? Were there any uncertainties or limitations in your equipment or techniques? It would also be useful to see the calculations and values used in the theoretical formula to see if there were any errors or discrepancies there.

In any case, it is important to carefully analyze and evaluate both the experimental and theoretical methods to determine the source of the discrepancy. It is possible that the experimental value is more accurate, but it is also important to consider any potential sources of error in the experimental setup. I would recommend discussing this with your teacher and/or conducting further experiments to confirm the accuracy of your results.

I hope this helps and good luck with your research!

 

[astrokreng]

Hi,

Thank you for sharing your experiment and results. It is not uncommon to see a discrepancy between theoretical and measured values in scientific experiments, and there are a few possible explanations for this.

Firstly, it is important to note that theoretical calculations are based on ideal conditions and assumptions, which may not always hold true in real-life experiments. So, it is possible that the assumptions made in the theoretical calculation are not completely accurate for your specific inductor.

Secondly, there may be some systematic errors in your experimental setup that could have affected the measured value. For example, there could be resistance in the wires or connections that could have influenced the current and therefore the calculated inductance.

Additionally, there could also be random errors in your measurements, which can be caused by factors such as human error or fluctuations in the equipment used.

It is also worth considering the precision of your measurements and calculations. The small difference between your measured value and the theoretical value could be due to rounding errors or uncertainties in your measurements.

In conclusion, it is important to carefully consider all the possible sources of error in both your theoretical calculations and experimental setup when comparing results. It is also helpful to repeat the experiment multiple times to ensure the accuracy and consistency of your results.