Why does current need to vary in an inductor?

[mcastillo356]

In a power transformer, the variation of the current in one circuit induces a current in the other. This cause-effect relationship is two ways. If circuit A affects circuit B, then B circuit will affect A circuit; this is the cause of the concept of mutual inductance. However, it's not necessary to consider two circuits. As the image shows, one circuit can induce a current by itself; this is called self-inductance. In this section,(it's a quote from a book) we are going to deal with inductors or bobbins, which are devices designed specifically to take advantage of self-inductance phenomenon. Normally, it's about multi-coiled bobbins. At first, we are going to describe with words how does work the induction bobbins. Let's suppose that a external power-source brings current to the bobbin of the figure. If current increases, so will do the magnetic flow that crosses the bobbin; therefore it will be an induced electromotive force that, according to Lenz's law, it will tend to oppose to that variation. The conclussion is a slowdown in the rate of increase of the current. To the contrary, if external energy source reduces, so will do the flow. To oppose to that variation, induced e.m.f. will "help" now the current to continue flowing. In both cases, the outcome is similar: the induction limits the rate in which current varies.
But first of all current must increase or decrease in the bobbin. Why?

 

[Delta2]

Summary:: In induction bobbins, current flows, and varyes: increases and decreases; Lentz's law rules to moderate this fact. But, in which way the current increases and decreases at first in the induction bobbins?

In a power transformer, the variation of the current in one circuit induces a current in the other. This cause-effect relationship is two ways. If circuit A affects circuit B, then B circuit will affect A circuit; this is the cause of the concept of mutual inductance. However, it's not necessary to consider two circuits. As the image shows, one circuit can induce a current by itself; this is called self-inductance. In this section,(it's a quote from a book) we are going to deal with inductors or bobbins, which are devices designed specifically to take advantage of self-inductance phenomenon. Normally, it's about multi-coiled bobbins. At first, we are going to describe with words how does work the induction bobbins. Let's suppose that a external power-source brings current to the bobbin of the figure. If current increases, so will do the magnetic flow that crosses the bobbin; therefore it will be an induced electromotive force that, according to Lenz's law, it will tend to oppose to that variation. The conclussion is a slowdown in the rate of increase of the current. To the contrary, if external energy source reduces, so will do the flow. To oppose to that variation, induced e.m.f. will "help" now the current to continue flowing. In both cases, the outcome is similar: the induction limits the rate in which current varies.
But first of all current must increase or decrease in the bobbin. Why?

I am not sure what a bobbin(?) is but if it is just any circuit element in which we have self inductance then ok.
I think the current in the bobbin will tend to increase or decrease due to the voltage (or current) source that is present in the circuit. But the self induction "doesn't let the source do the job alone" it plays its role in the increase or the decrease of the current.

 

[Merlin3189]

I think a bobbin is a coil.

 

[Merlin3189]

I once had similar introspections about transformers, until I came across a web site, Elliott Sound Products, which has a lot of explanation about transformers. Rod Elliott was good enough to respond to some of my questions and changed my thinking about transformers. (But don't blame him for anything I now say!)

I have done away with the idea that anything causes anything else in transformer currents. There is a mathematical relationship between primary and secondary and they can't change independently.

If the secondary current changes, perhaps a change in load resistance, so does the primary current.
If the primary current changes, perhaps a change in source resistance, so does the secondary current.
We can ascribe cause and effect, and think one changes before the other, but in reality, they change simultaneously because they are all part of one circuit.

Compare a simple series circuit with two variable resistors (and a constant voltage source.) There is a current flowing through both resistors. If you vary either one, the current changes in both of them simultaneously. Doesn't even need to be the same number of electrons in each, if we introduce a parallel resistor. The currents are now different, but still change together.

It is not the same electrons in each resistor - different electrons linked by electric field.
Just as in a transformer, different electrons in primary and secondary, linked by magnetic field.

Coming to your single inductor - bobbin, coil, choke - and the relation between emf, flux and current: again they are all mathematically related. It is no more helpful to ascribe cause and effect here. The relationship is more complex, due to the differential, but it is a mutually deterministic mathematical relation between all three.

The desciption you give from the book is much as I might describe things in a casual way. But the impression of cause and effect is misleading. It is just decribing the mathematical connection between the variables.
Lenz's law does not describe the psychology of conductors wanting to oppose changes of flux, nor the order in which changes happen. It simply says what the direction of emf IS when flux is changing.

...an external power-source brings current to the bobbin ... If current increases, so will do the magnetic flow that crosses the bobbin; therefore it will be an induced electromotive force that, according to Lenz's law, it will tend to oppose to that variation. The conclussion is a slowdown in the rate of increase of the current.

... current from a power source flows in the bobbin. If current increases, magnetic flux increases. As flux is increasing, there is an emf. Lenz says the emf is in the opposite direction to the current. At every instant that emf exactly matches the applied emf from the source. Conclusion: if you apply a constant emf to a pure inductance you get a constant rate of change of current.

The reason we may see an effect, "a slowdown in the rate of increase of the current", is dependent on the source resistance and/or on resistance of the bobbin (which can be combined.) As the current increases, IR voltage drop in the resistance increases, so the applied emf to the inductance decreases and the back emf must identically be decreasing, so the rate of change of flux must be similarly decreasing and the rate of change of current must be decreasing. All mutually deterministic.

...the induction limits the rate in which current varies.

The inductance determines the rate at which current varies, $\frac{dI}{dt}=\frac{V}{L}$
If I apply 10 V to a 1 H inductor, the current immediately IS increasing at 10 A/sec and continues to do so as long as I apply the 10 V. It is only the non-ideal features of the voltage source and the real inductor, that causes the limit he refers to.
It is one of the sad facts of electronic life, that all practical inductors have resitance and this is often much more significant than the similar departures from the ideal in resistors and capacitors.

 

[Dale]

Summary:: In induction bobbins, current flows, and varyes: increases and decreases; Lentz's law rules to moderate this fact. But, in which way the current increases and decreases at first in the induction bobbins?

But first of all current must increase or decrease in the bobbin. Why?

For the example given it increases or decreases due to an external power source. It says “Let's suppose that a external power-source brings current to the bobbin of the figure. If current increases, ...”

 

[mcastillo356]

Ok, I've got a circuit: a power source and a resistance, and a coil. The power source increases current, the resistance will decrease current flow, and the coil, that limits the rate the current varies. I've understood?

 

[Dale]

Ok, I've got a circuit: a power source and a resistance, and a coil. The power source increases current, the resistance will decrease current flow, and the coil, that limits the rate the current varies. I've understood?

Essentially, except that I am never comfortable with saying that a resistance "decreases" current flow. Basically it makes a voltage and current proportional to each other. I realize that "decreases" is easier to say than "makes proportional to voltage", but it is important to keep in mind the physics instead of the easy phrasing.

 

[Delta2]

Essentially, except that I am never comfortable with saying that a resistance "decreases" current flow. Basically it makes a voltage and current proportional to each other. I realize that "decreases" is easier to say than "makes proportional to voltage", but it is important to keep in mind the physics instead of the easy phrasing.

In RLC circuits the resistance limits the current, it appears on the denominator of the formula of the current like for example in the formula $$I=\frac{V_0}{R}(1-e^{-t\frac{R}{L}})$$ or $$I=\frac{V_0}{\sqrt{R^2+(\omega L-\frac{1}{\omega C})^2}}e^{j\omega t+\phi}$$
so I think there is nothing wrong to say that the resistance decreases the current flow. And is also in accordance with the intuitive picture we have (resistance means collisions of the free electrons with the ions of the conductor during which they lose momentum and kinetic energy).

 

[anorlunda]

Ok, I've got a circuit: a power source and a resistance, and a coil. The power source increases current, the resistance will decrease current flow, and the coil, that limits the rate the current varies. I've understood?

As @Merlin3189 said, the relationships such as I=V/R are circular and simultaneous. It is wrong to impose a sequential cause-effect relationship on top of that. If I think of R as the ratio of V/I, that does not mean that 1) we have V, which 2) causes I, which 3) causes R. That would be wrong.

I have done away with the idea that anything causes anything else in transformer currents. There is a mathematical relationship between primary and secondary and they can't change independently.

So instead of confirming the sequence of events as you state it, we are saying "don't think of it as a sequence."

 

[mcastillo356]

Thank you very much everybody. You've done what I thought impossible: make me understand!