# Nature of inductance, solenoids and transformers

1. Jun 16, 2007

### Mr_Bojingles

On wikipedia they give a fairly simply explanation of inductance
But on http://www.electronics-tutorials.com/ they give a different definition
I dont understand the latter there. Theyre saying any solenoid resists current and the higher the inductance the higher the resistance?

Another question regarding transformers. From what Ive read the voltage produced in the second coil is directly proportiate to the ratio of windings in each coil. I know that the more windings in the first coil the greater the magnetic flux hence the greater the current induced in the second coil but what I dont understand is how come more windings on the second coil produces higher voltage?

Is it solely because theres more wire within the range of the first coils magnetic field or are there other factors involved?

2. Jun 16, 2007

### ice109

yup more coils means more flux

this equation says a lot $$\varepsilon = -L\frac{di}{dt}$$

3. Jun 16, 2007

### ranger

Mr_Bojingles,
The second definition is much more elegant to understand and reflects the true nature of inductance. However, I would change what you said slightly to a solenoid resists changes in current. A solenoid would pass DC current with no problems, however when we have a change in current, the solenoid would oppose these changes in accordance with Lenz's Law.

4. Jun 17, 2007

### NoTime

The wire does not have to be in a coil.
A straight piece of wire has inductance.

5. Jun 22, 2007

### Mr_Bojingles

I read a few tutorials on it but I still don't fully understand it.

If my calculations are correct a changing current flowing through the solenoid on the right will induce current in the solenoid circuit on the left which will trigger the needle on the compass to move.

So in this case is the inductance the ratio of magnetic flux on the left (compass) solenoid to the current flowing through the right solenoid?

Would the measure of both flux and current on the right solenoid be called self inductance instead? Since a current is induced on the left solenoid which induces a magnetic field could you call that the self inductance of the left solenoid?

I think I understand why inductance opposes any change in current. Lets say I have a circuit with 50 amps applied to it but the changing magnetic flux induces a counter EMF which brings it down to 30 amps. If I double the initial EMF so I'm applying 100 amps then the magnetic flux will also double along with doubling the counter EMF so the current stays at 30 amps? Is that correct?

Last edited: Jun 22, 2007
6. Jun 23, 2007

### NoTime

Yes, but any current in the left half will quickly cease.

Inductance is a quantity by construction.
It affects current, but is not modified by current.
I suspect you may be confusing turns ratio in a transformer here. This has to do with voltage out of a transformer (the central device) vs voltage in.
Current is controlled by impedance, which can be more or less thought of as resistance.

I have no idea of what you are trying to say here.

Sorry - This is really confused.
You are mixing up the concepts of voltage an current.
EMF is voltage not current.
If you apply 10 volts to the coil initially the reverse voltage will be 10 volts (back EMF) and current will be zero.
If you apply 100 volts to the coil initially the reverse voltage will be 100 volts and current will still be zero.

7. Jun 23, 2007

### Mr_Bojingles

Ah yeah I got it mixed up. I was trying to understand how inductance is the property of opposing any change in current.

What I was reading is that when a changing magnetic field induces a voltage in a circuit that induced voltage is in the opposite direction of the voltage that caused the magnetic field.

For example I have a basic circuit. I apply 100 volts AC to it. This creates a magnetic field and since the AC current is fluctuating the magnetic field is also fluctuating. This changing magnetic field then induces a secondary EMF in the circuit but this secondary EMF is in opposition to the initial 100 volt EMF.

Have I got the concept wrong?

8. Jun 23, 2007

### xez

I haven't closely followed this whole discussion, so
forgive me if I miss some previous contextual
point or am redundant.

Here's pretty much what you ought to know about
the concepts of practically understanding and
using inductance:

* Inductance measures the magnetic flux produced per
amount of current present in a circuit element.

* Knowing the current in and inductance of
and geometry of an inductor tells you the shape and
strength of the magnetic field around that inductor,
and that'd be what's relevant for something like an
electromagnet.

* Knowing the current and inductance of a
magnetically isolated inductor will tell you the energy
stored in the magnetic field of that inductor. This is
applicable mostly to single isolated 'coils' / 'inductors'
whose primary purpose is to have inductance,
and isn't generally the way you'd use / understand a
transformer overall since the main point of a transformer
isn't the inductance of its windings taken INDIVIDUALLY,
but is the COUPLING properties of signals or power
between its windings.

* Knowing the inductance of a magnetically isolated
inductor is also relevant if you're using that inductor
as a 'choke' or in a R-L or L-C filter or resonator circuit.

* Inductors that are designed to be highly coupled via
their magnetic fields to other inductors or conductive
objects in their environment are generally analyzed by
more attributes than just their inductance since the
significant magnetic field coupling and the uses that
is being put to is generally the most relevant thing
there. This would cover things like transformers,
metal detectors, et. al. When two inductors are
magnetically coupled they're said to have a
MUTUAL INDUCTANCE which is a true value of inductance
relating the field induced in the OTHER inductor by a
current in the FIRST. The mutual inductance between two
objects is a recriprocal thing, and depends geometrically
on the relative positions and windings of BOTH inductors;
it becomes not sufficient to talk about the INDIVIDUAL
inductances of coupled inductors since the presence of
a circuit on the coupled inductors effects the perceived
inductance of any single one of them.
Hence in idealized transformers you start to look at
things like "turns ratios" and "degree of coupling"
and "mutual inductance" as being mostly relevant rather
than the individual coil inductances ignoring coupling
effects.

* For isolated inductors in idealized cases you just
ignore the "self inductance" type of considerations
of how the magnetic field of the inductor itself
actually relates to the component's own coils etc.
Saying "the inductance of this inductor is L" is
enough to use that component in a simple circuit.
Using circuit equations relating to things like
time constants, resonance frequencies, Quality Factor Q,
complex Impedance, et. al. is directly possible knowing
JUST the (L) value of inductance. Similarly in
idealized cases you assume that there is NO relevant
coupling of the magnetic field of that inductor to
any other part of your circuit or conductive object.
Having a value of (L) and being able to say that it's
an isolated inductor is enough for all circuit analysis.
This FAILS to be true in 'extreme cases' of high
frequencies when you'll find that the value of Inductance
actually varies with frequency, and actually what one
naively assumes is basically a simple coil/inductor
does not behave like a PURE inductor but actually behaves
like a complicated little circuit containing resistance,
capacitance, and inductance all together. This is only
relevant for high frequencies usually above 50,000 Hz,
or for very poorly constructed inductors. For DC to several
kilohertz frequency analyses with well constructed
inductors, just use the inductance (L) in the equations
and it'll tell you all you need to know.

* So with respect to your concept of 'secondary' EMFs
or actually EMFs at all, that'd be mostly
an analysis you'd use to understand some kind of
magnetically coupled inductive circuit where some
given or assumed magnetic field acts as an 'external'
stimulus on some inductors or circuit coils/paths/loops
and generates an EMF. If you had a permanent magnet
and a loop of wire moving in its field acting as a generator,
or you wanted to design a transformer, etc. that's the
kind of analysis you'd do (coupled / induced EMFs).
For two-terminal simple circuit analysis, though,
you's treat each resistor (R), capacitor (C), inductor (L)
as a two-terminal device COMPLETELY specified by
its resistance, capacitance, inductance (respectively)
and you'd wholly IGNORE field-coupling considerations
due to coupled fields between circuit elements or the
influence of or generation of fields external to the
circuit, since that's beyond isolated circuit analysis.
You could of course use circuit analysis to analyze the
response of a circuit to a given 'external' EMF or 'external'
field causing an EMF in an inductor, though, if you were
building something like a generator driven circuit or
magnetic field meter or whatever.

* To the extent that you want to understand the
circuit analysis relevant ways that inductors,
resistors, capacitors behaves in a circuit, study things
like Ohm's law, the thevenin theorem, concepts of
complex impedance, phase angle, phasors, reactance,
parallel circuits, series circuits, resonant circuits, etc.
Basically there are very simple equations that tell you
how DC or single frequency sine wave AC voltage
sources behave when you have R, C, L circuits, and
how specific values of voltage and current become present
across each 2-terminal element (R, C, L) of the circuit.
In AC analysis you'll learn that inductive circuits have
voltage waveforms leading the current waveform in phase
(we're talking about single frequency sine waves here),
and capacitive circuits have voltage waveforms lagging
the current waveform. For purely resistive AC circuits
the voltage and current are in phase. Inductive reactances
are assigned to positive Y-axis reactance values in
the complex plane, capacitive reactances are assigned
negative Y-axis values in the complex plane, and
resistors get positive X-axis values in the complex plane.
So resistors have positive real number
resistance values associated, and capacitve reactances
are negative imaginary numbers, and inductive reactances
are positive imaginary values. Then you can do things
like use algebraic geometry to calculate phase angles,
vector magnitudes, parallel and series combinations.
You'll see that capacitive and inductive reactances in
series cancel out (because one is positive and the other
is negative), and that resonance can occur if capacitive
reactance is equal to inductive reactance, etc. etc. etc.

* Generally you only use EMF and magnetic field
based analysis for understanding motors, transformers,
sensors, generators, and electromagnetic theory in
general. Study magnetostatics, maxwell's equations,
electrostatics, lotentz force, ampere's law, lenz's law,
biot-savart law, etc. etc. to discover the ways you calculate
electric and magnetic fields due to charges and currents,
how fields add linearly in 2D/3Dvector space, how you'd
calculate inductance or capacitance of a geometrical
object, vector potential of the static magnetic field,
curl of the magnetic field, etc. etc. It's really more
about electromagnetic physics than relevant to circuit
analysis in that domain.

9. Jun 23, 2007

### xez

Oh and as a quick addendum:

An induced current in an inductor will create a field
that opposes the change in the external field.

So if the external field is increasing in front of
a loop, let's say because that there's the north pole
of a bar magnet physically approaching a closed coil
inductor, then the induced current will induce a north
pole on the side near the oncoming north pols, so the
two facing north poles repel (mechanically) each
other, and the overall increase of flux through the
loop because of the external field is lessened by the amount
of the induced field.

If the same external magnet with its north pole facing
the coil started to recede, thus lessening the flux of its
magnetic field through the loop, a current would be
induced in the loop that would form a south pole
near the external magnet's nearby receding face (whch
is a north pole). The magnet's receding north pole would
be attracted to the induced south pole, and the overall
flux through the coil would be increased by the induced
current which is opposing the decrease of the field
due to the receding magnet.

You can analyze inductive circuits with respect only to
the external field and the known inductance of the
inductor whose action is being determined; you don't
in general simplistic cases consider the action of
the induced field ON the inductor that's INDUCING the
field; you know its 'response' to the external stimulus
based on its 'lumped sum' values of inductance etc.
and you're using those to say what its passive response
will be relative to an 'external' field / stimulus.

The fact that circuit theory assigns the quantity of
reactance to an inductor based upon the
sinusoidal frequency and the inductance accounts wholly
for the action of the self-induced EMF, so considering
the self induction EMF is 'true' it's important to understand
that that's the MECHANISM by which a voltage 'drop'
or 'source' is assigned to an inductor in a circuit based
on its known reactance. So the simplified consideration
of just saying that there's an inductive reactance of
N ohms is sufficient when the inductor is responding
to an applied CIRCUIT VOLTAGE.
Saying that you have an inductor in series with an ideal
voltage source of V volts is sufficient (relative to
circuit response) to describe the case where induced
voltage in a coil is coupled to a circuit. And in the
case of a transformer, you use various transformer
circuit equivalent circuit models or equations to figure
out the circuit relevant behavior -- the induced field
and EMFs are be essential to the physics, but
circuit theory gives you circuit theoretic models that
account for the field coupled behaviors without
the need to model them in literal/physical detail.

10. Jun 23, 2007

### NoTime

I think you have half the picture.
You should try thinking of an inductor as an energy storage device.
An inductor will try to maintain the current as the magnetic field collapses.

What happens with a stand alone coil when you open the switch?

Say in your attachment, when you switch off the device, the needle will once again deflect.
But, there is a difference.
What is the difference?

11. Jun 25, 2007

### Mr_Bojingles

Thanks alot NoTime. That pretty much explains everything.

12. Jul 14, 2007

### dawog

Where can inductance be used to benefit and installation?

And also operating principals of induction motors?

13. Jul 14, 2007

### ranger

One example would be to use an inductor to prevent damages to a load due to rapid changes in current/current spikes. These inductors are called chokes.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indmot.html

14. Jul 15, 2007

### dawog

is high power factor good or bad? and why?

15. Jul 15, 2007

### ranger

Do not repost the same question twice; especially if its a homework question.