# Resistive Characteristics Of a Coil in Changing Magnetic Field

#### positive8

Joined Sep 27, 2016
61
In a purely resistive circuit consisting of a coil and a resistor in series, in which a magnet is passed through the coil generating a single sinusoidal cycle of low frequency (thus behaving essentially as a DC signal in terms of impedance, etc.), is the total resistance of the circuit simply the addition of the resistance of the resistor and the coil? Or does the single pulse behave like a waveform generated by a signal generator as it "travels" through the resistor?

#### Papabravo

Joined Feb 24, 2006
16,509
In a purely resistive circuit consisting of a coil and a resistor in series, in which a magnet is passed through the coil generating a single sinusoidal cycle of low frequency (thus behaving essentially as a DC signal in terms of impedance, etc.), is the total resistance of the circuit simply the addition of the resistance of the resistor and the coil? Or does the single pulse behave like a waveform generated by a signal generator as it "travels" through the resistor?
You cannot have a purely resistive circuit if there is a coil involved. What you can do, is ask what happens in the limit, as the inductance goes to zero. This is equivalent to changing the coil into a shorter and shorter wire. You could also investigate what happens as:

$$\omega L \rightarrow 0$$

This will obliterate the frequency dependence and the effect of the coil inductance

#### positive8

Joined Sep 27, 2016
61
You cannot have a purely resistive circuit if there is a coil involved. What you can do, is ask what happens in the limit, as the inductance goes to zero. This is equivalent to changing the coil into a shorter and shorter wire. You could also investigate what happens as:

$$\omega L \rightarrow 0$$
The inductance is negligible in this circuit. I calculated it and it was in the very low microhenries, which can be ignored. Everything I've read says this is essentially a resistive circuit, my question revolves around whether the exiting single sinusoidal waveform voltage characteristics are shaped by the total resistance of the circuit, or only by the resistivity of the coil and the rate of change of the magnetic flux?

#### Papabravo

Joined Feb 24, 2006
16,509
The inductance is negligible in this circuit. I calculated it and it was in the very low microhenries, which can be ignored. Everything I've read says this is essentially a resistive circuit, my question revolves around whether the exiting single sinusoidal waveform voltage characteristics are shaped by the total resistance of the circuit, or only by the resistivity of the coil and the rate of change of the magnetic flux?
If the inductance of the circuit is negligible then so is the AC voltage produced by the moving magnet. The shape of the waveform kinda depends on what the rest of the circuit looks like. How about a diagram of what you have in mind.

For example: If L= 1 μH and di/dt = 1 μA/sec, then the voltage across the inductor will be 1 pV RMS. Is 1 pV significant or not?

Let di/dt = 10 A/msec, now the voltage across the inductor is 10 mV RMS. Is 10 mV RMS significant or not?

Finally let di/dt be 10 A/μsec, now the voltage will be 10 V RMS. Is that significant?

No mater how small the inductance there is a time rate of change of current that will produce a substantial voltage. Can you achieve that time rate of change of current with a magnet? It depends on the magnet.

You need to specify your problems with more precision.

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#### cmartinez

Joined Jan 17, 2007
7,378
How about a diagram of what you have in mind.
And some values ... to see what he means by

I calculated it and it was in the very low microhenries, which can be ignored.

#### tranzz4md

Joined Apr 10, 2015
310
The inductance is negligible in this circuit. I calculated it and it was in the very low microhenries, which can be ignored. Everything I've read says this is essentially a resistive circuit, my question revolves around whether the exiting single sinusoidal waveform voltage characteristics are shaped by the total resistance of the circuit, or only by the resistivity of the coil and the rate of change of the magnetic flux?
No, not at all. If the inductance can be ignored, so can your question. You are actually dealing with that finite inductance and finite impedance.

(I'm asking myself why I didn't ignore this,,,, but find my reasons negligible)

#### positive8

Joined Sep 27, 2016
61
That kinda depends on what the rest of the circuit looks like. How about a diagram of what you have in mind.
Simple as it gets, one small coil and one small resistor in series (although they are essentially in a loop). A bar magnet within the coil moves and generates an EMF. a single sinusoidal waveform is generated and propagates through the resistor.
Know all about Faraday's and Lenz's Laws, etc., I'm just curious if the emitted waveform acts like a battery source with an internal resistance with a fixed voltage due entirely to magnetic flux action confined within the coil and THEN acts on the resistor, or whether the combined resistance of the coil and the resistor affect the single waveform characteristics emitted from the coil?

#### positive8

Joined Sep 27, 2016
61
No, not at all. If the inductance can be ignored, so can your question. You are actually dealing with that finite inductance and finite impedance.

(I'm asking myself why I didn't ignore this,,,, but find my reasons negligible)
???? Guess I must be stupid or something, because I couldn't make head or tail of your answer. I'm very sorry if the simple-minded nature of my question offends you. I'm at a very elementary level of knowledge, as you can tell, but, if someone asks me a question, I always make an effort to be gracious and respond to the best of my ability. Or simply not respond. I'm guess I'm underqualified for this forum and should leave quietly. I didn't know at the time of signing up basic questions were discouraged.
I have read repeatedly that impedance issues can be ignored in largely resistive circuits, and this qualifies, I'm sure. The question revolved around the "black box" nature of the coil relative to the remainder of the circuit.

#### Papabravo

Joined Feb 24, 2006
16,509
So the coil and the resistor are in parallel. Whatever waveform is created in the coil, will likely be very minimal, and will be dissipated in the resistor via KVL. The sum of voltages around a closed loop must be zero.

#### positive8

Joined Sep 27, 2016
61
So the coil and the resistor are in parallel. Whatever waveform is created in the coil, will likely be very minimal, and will be dissipated in the resistor via KVL. The sum of voltages around a closed loop must be zero.
I'm getting 30-40 Vpp out of the coil. I know the velocity and intensity of the magnetic field of the magnet. The measured characteristics match the results of the equation very closely. I was not quite sure whether this would be seen as a parallel or series circuit, so thanks very much for cluing me in there.
The other mystery, and the main point of my question, was does the emitted waveform act like a waveform generated by a signal generator relative to the circuit as a whole, or is the waveform voltage "incorporating" the parallel resistance of the coil and resistor?
I'm guessing it's the latter, but, given the the magnetic actions being confined within the coil, I didn't know if resistive elements outside the coil may play a lesser role?

#### tranzz4md

Joined Apr 10, 2015
310
No offenses taken, whatsoever. Simply, do "the math". You did. Then what? You ignore the answer?

We are dealing with finite reality here. I may well misunderstand your question, but I don't believe ignoring the calculations will help acquire a useful answer, or aid understanding. The same "they" that said that "impedance issues can be ignored....." said "a coil cannot be present in a purely resistive circuit".

Sarcastic humor, unfortunately, doesn't carry well in this medium, so I apologize for any particular irritation my parenthetical remarks may have caused you. (I'm glad a few chuckles were had elsewhere.....

#### cmartinez

Joined Jan 17, 2007
7,378
So the coil and the resistor are in parallel. Whatever waveform is created in the coil, will likely be very minimal, and will be dissipated in the resistor via KVL. The sum of voltages around a closed loop must be zero.
Say, could this sort of thing be reliably simulated in LTspice? ... a noobie could learn tons of things by just playing with a model like this one for a few minutes .

#### Papabravo

Joined Feb 24, 2006
16,509
Say, could this sort of thing be reliably simulated in LTspice? ... a noobie could learn tons of things by just playing with a model like this one for a few minutes .
I believe a resistor and a behavioral voltage source (current source) might do the trick.

#### positive8

Joined Sep 27, 2016
61
No offenses taken, whatsoever. Simply, do "the math". You did. Then what? You ignore the answer?

We are dealing with finite reality here. I may well misunderstand your question, but I don't believe ignoring the calculations will help acquire a useful answer, or aid understanding. The same "they" that said that "impedance issues can be ignored....." said "a coil cannot be present in a purely resistive circuit".

Sarcastic humor, unfortunately, doesn't carry well in this medium, so I apologize for any particular irritation my parenthetical remarks may have caused you. (I'm glad a few chuckles were had elsewhere.....
Someone sent me an email apologizing on your behalf and saying you had an established reputation as a jerk.
I did do the equations. And you did NOT understand the technical basis behind my question, unlike the other responders.

#### Papabravo

Joined Feb 24, 2006
16,509
I'm getting 30-40 Vpp out of the coil. I know the velocity and intensity of the magnetic field of the magnet. The measured characteristics match the results of the equation very closely. I was not quite sure whether this would be seen as a parallel or series circuit, so thanks very much for cluing me in there.
The other mystery, and the main point of my question, was does the emitted waveform act like a waveform generated by a signal generator relative to the circuit as a whole, or is the waveform voltage "incorporating" the parallel resistance of the coil and resistor?
I'm guessing it's the latter, but, given the the magnetic actions being confined within the coil, I didn't know if resistive elements outside the coil may play a lesser role?
It would really help if you would start drawing diagrams instead of writing hard to parse paragraphs describing circuits. Component values matter. Also I have no idea what "act like a waveform generated by a signal generator" means. What does that phrase mean to you?

#### positive8

Joined Sep 27, 2016
61
I believe a resistor and a behavioral voltage source (current source) might do the trick.
I think it would, sure. I'm already sending very powerful magnets at many meters/sec through varying coils and across different resistor loads and getting results consistent with the equations. I was just curious about the nature of the physics within the coil and it's effects on the remainder of the circuit, PARTICULARLY in terms of a single-shot waveform and whether that varies relative to a longer-term cyclical modulation of the magnetic field.
I believe I have enough lab equipment I can get my hands on to simulate this....................
(And NO, I am not building a rail or coil gun...........)

#### BR-549

Joined Sep 22, 2013
4,938
The resistance is in series. The voltage waveform of the resistor is a mirror of the magnet movement relative to the coil.

#### positive8

Joined Sep 27, 2016
61
The resistance is in series. The voltage waveform of the resistor is a mirror of the magnet movement relative to the coil.
Aha, is it? Picture a coil and a resistor place side by side
It would really help if you would start drawing diagrams instead of writing hard to parse paragraphs describing circuits. Component values matter. Also I have no idea what "act like a waveform generated by a signal generator" means. What does that phrase mean to you?
Sure,sorry, but here we're talking about two components - a coil and a resistor - connected serially by wires. Your point is well taken, but in this case the circuit is very simple and I'm sure you can visualize it.
"Act like a waveform generated by a single generator" means to me a waveform generated by a signal generator should be regulated in amplitude, frequency,etc., regardless of load, just like a DC battery (within operational levels). This is not the case in a dynamic circuit composed of various types of components responding differently in a fluctuating voltage.
You are actually helping me to define my question more accurately, though. To wit," Do the physical effects taking place within a coil in a fluctuating magnetic field that consequently generate a single EMF waveform act independently of the remainder of the components in a circuit experiencing NO electrical activity prior to the generation of the waveform by induction".

#### BR-549

Joined Sep 22, 2013
4,938
"Aha, is it? Picture a coil and a resistor place side by side"

Draw a picture.

Where does the current split? Or fork.

#### Papabravo

Joined Feb 24, 2006
16,509
Without component values it is hard to evaluate or double check your observations. For the coil, how about the diameter and the number of turns. For the magnet, some indication of field strength, velocity, and frequency of motion.