# I’m confused as to how to find the Inductance of my coil in RL circuit!

#### Hazzafez

Joined Mar 8, 2020
3
I have an a.c sig gen with an inductor, resistor in series and an o.c.r in parallel. I have measured frequency and voltage across the coil. How do I find the reactance and inductance of the coil without using the equation L=(m x N^2x pi x r^2)/l ??
I know XL=2pifL and for an RL circuit (current through L)=VL/(root R^2+XL^2).
im stuck as to how to get there, it’d be amazing if you could help me
thank you very much!

Joined Mar 10, 2018
4,057
Whats an o.c.r. ?

Regards, Dana.

#### peterdeco

Joined Oct 8, 2019
220
I never tried this so I don't know how accurate it is but I was told if you put the inductor in series with a potentiometer and adjust the pot until you get 1/2 the voltage where the 2 connect with an oscilloscope, the pot value will be the same resistance as the inductor at that frequency. Finding the inductor value should then be easy. The easiest thing is to just get an inductance meter.

#### Jony130

Joined Feb 17, 2009
5,181
and adjust the pot until you get 1/2 the voltage
Well, in this case the inductance value will be equal to:

$L=\sqrt{\frac{1}{3}}\frac{R}{2\pi f}$

And this equation is true only for a frequency at which the (Vgen/Vinductance) = 0.5

#### Hazzafez

Joined Mar 8, 2020
3
Whats an o.c.r. ?

Regards, Dana.
Sorry, I meant c.r.o cathode ray oscilloscope

#### SamR

Joined Mar 19, 2019
2,541
Let's back up, what values do you have? Vrms=?, Rmeas=?, f=?, L=?, Pi=3.14

#### MrAl

Joined Jun 17, 2014
7,799
I never tried this so I don't know how accurate it is but I was told if you put the inductor in series with a potentiometer and adjust the pot until you get 1/2 the voltage where the 2 connect with an oscilloscope, the pot value will be the same resistance as the inductor at that frequency. Finding the inductor value should then be easy. The easiest thing is to just get an inductance meter.
Hello,

That does not seem to work. However, assuming a sinusoidal test wave when the measured voltage is 1/2 of the applied voltage:
L=R/(2*pi*sqrt(3)*f)

So if R is 10.883 Ohms and f=1000Hz then:
L=10.883/(2*3.14159*1.732*1000)
L=0.001 Henries

Alternately:
L=R/10.883/f

The voltage across each element is also interesting:
vL=(2*pi*f*A*L)/sqrt(R^2+4*pi^2*f^2*L^2)
vR=(A*R)/sqrt(R^2+4*pi^2*f^2*L^2)

where A is the amplitude of the test sine wave.
Note that when vL=vR each voltage is A/sqrt(2) not A/2.
So vL+vR is not equal to A but is equal to sqrt(2)*A.

• Hazzafez

#### MrAl

Joined Jun 17, 2014
7,799
I have an a.c sig gen with an inductor, resistor in series and an o.c.r in parallel. I have measured frequency and voltage across the coil. How do I find the reactance and inductance of the coil without using the equation L=(m x N^2x pi x r^2)/l ??
I know XL=2pifL and for an RL circuit (current through L)=VL/(root R^2+XL^2).
im stuck as to how to get there, it’d be amazing if you could help me
thank you very much!
Hi,

That assumes a sinusoidal test wave and a meter that can read AC voltages at the generator frequency without much error or an oscilloscope.

#### BobaMosfet

Joined Jul 1, 2009
1,207
I have an a.c sig gen with an inductor, resistor in series and an o.c.r in parallel. I have measured frequency and voltage across the coil. How do I find the reactance and inductance of the coil without using the equation L=(m x N^2x pi x r^2)/l ??
I know XL=2pifL and for an RL circuit (current through L)=VL/(root R^2+XL^2).
im stuck as to how to get there, it’d be amazing if you could help me
thank you very much!

#### BobaMosfet

Joined Jul 1, 2009
1,207
@Hazzafez

Inductance Calculations
Author: Frederick W. Grover
ISBN-10: 048647440-2

#### MrAl

Joined Jun 17, 2014
7,799
@Hazzafez

Inductance Calculations
Author: Frederick W. Grover
ISBN-10: 048647440-2
That's way more than he is looking for i believe.

#### SamR

Joined Mar 19, 2019
2,541
I think he wanted a quick answer, not help...

#### MrAl

Joined Jun 17, 2014
7,799
I think he wanted a quick answer, not help...
Hi,

Yeah and Grover's book is detailed calculations through tables for physical constructions.
It's an interesting book though.

• SamR

#### Hazzafez

Joined Mar 8, 2020
3
Hello,

That does not seem to work. However, assuming a sinusoidal test wave when the measured voltage is 1/2 of the applied voltage:
L=R/(2*pi*sqrt(3)*f)

So if R is 10.883 Ohms and f=1000Hz then:
L=10.883/(2*3.14159*1.732*1000)
L=0.001 Henries

Alternately:
L=R/10.883/f

The voltage across each element is also interesting:
vL=(2*pi*f*A*L)/sqrt(R^2+4*pi^2*f^2*L^2)
vR=(A*R)/sqrt(R^2+4*pi^2*f^2*L^2)

where A is the amplitude of the test sine wave.
Note that when vL=vR each voltage is A/sqrt(2) not A/2.
So vL+vR is not equal to A but is equal to sqrt(2)*A.

I am currently doing a personal investigation on inductors and seeing how the inductance and current changes with the number of coils of wire, core radius and material of core. If I could somehow find out the inductance of each inductor by not using the formula (L=mN^2pir^2) and then comparing results to measure the uncertainty in my results it would be ideal. I attach some of my results so that you may see my progress

in #7 when you refer to R do you mean the impedance of the circuit or just the individual resistance of the variable resistor?
thank you very much!!

#### SamR

Joined Mar 19, 2019
2,541
Try solving it using the formula for coil inductive reactance.

#### peterdeco

Joined Oct 8, 2019
220
OK, I've never tried my earlier suggestion so I didn't know if it worked or not. This worked for me at radio frequencies. I never tried low audio frequencies. I took a capacitor of known value and put it in parallel with the inductor. This creates a tank circuit. Then I put an RF signal generator and oscilloscope in parallel. I swept the frequency until the voltage peaked across the coil. That is the resonant frequency of the tank circuit. Faster than doing the math, I used a chart with a ruler and intersected the frequency with the value of the capacitor. On the end of the ruler is the value of the inductor. There is a bunch of software that will do this. I once did it to determine the value of a .1uH inductor as the voltage peaked at 100MHZ - until I bought a capacitance/inductance meter. I just saw one on Amazon for \$33.99. It saves a lot of time.

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#### MrAl

Joined Jun 17, 2014
7,799
I am currently doing a personal investigation on inductors and seeing how the inductance and current changes with the number of coils of wire, core radius and material of core. If I could somehow find out the inductance of each inductor by not using the formula (L=mN^2pir^2) and then comparing results to measure the uncertainty in my results it would be ideal. I attach some of my results so that you may see my progress

in #7 when you refer to R do you mean the impedance of the circuit or just the individual resistance of the variable resistor?
thank you very much!!
Hello again,

Yes "R" is the fixed resistor value.
Is the value of the resistor you use in your charts always 100 Ohms?

Oh so you are building your own inductors and testing them in order to determine what the relationship the actual construction has to the inductance.

In this case the Grover book may help you a lot then because that is all done in that book or at least the ways to calculate various shapes and turns and the like are presented. You might like that a lot. The tables are derived from theory.

There may be some differences though because if you test one with various frequencies you will start to see the equivalent capacitance also creep into the calculation.

The formula for the inductance when measuring the center voltage of the fixed R with L and driven with a sinusoidal voltage source is:
L=(R*VL)/(2*pi*f*sqrt(A-VL)*sqrt(A+VL))
where
L is the inductance in Henries,
R is the fixed resistor value in Ohms,
VL is the measured voltage across the inductor in Volts,
f is the frequency in Hertz,
A is the amplitude of the driving sinusoidal voltage source in Volts,
pi is of course the constant 3.14159...
If you measure A in volts peak, then VL is also in volts peak.
If you measure A in volts RMS, then VL is also in volts RMS.

You can apply that formula to your measurements you posted and see what you get.
You may see a variation as you go up in frequency because of the equivalent capacitance. We could talk about that next if you like, but if you stick to the lower frequencies that wont affect the measurements too much.

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#### puppydog846

Joined Apr 5, 2020
11
Well, in this case the inductance value will be equal to:

$L=\sqrt{\frac{1}{3}}\frac{R}{2\pi f}$

And this equation is true only for a frequency at which the (Vgen/Vinductance) = 0.5

#### puppydog846

Joined Apr 5, 2020
11
if you have an frequency adjustable generator put compontes is series until the voltages across each one is equal not i/2 the generator then the inductor has the same impedance and their sun is sqrt 2 of the applies due to the phase shift
the. use your equation for Zl and solve for l