# transistors: so confusing!!

Discussion in 'Electronic Basics' started by andrew_h, Feb 9, 2006.

1. ### andrew_hGuest

I am new to electronics - I have learnt heaps and am enjoying every new
thing I'm learning. I did do Physics in school, but like alot of people
- didnt pay a HUGE amount of attention to things I learnt. Alot of it
has actually come back - now I wish I paid a bit more attention!

Something that has been confusing me no-end, and I just cant seem to
grasp, is how a TRANSISTOR works!!!

I have read many explanations, but they are confusing and vauge. People
have explained like a tap, that a small change in the base current
allows a much larger amount of current to flow through the
collector/emitter.

I cant grasp WHY they are so extremely important - probably because I'm
finding it hard to understand their basic operation !

Any help with this would be greatly appreciated ... this is really
proving to be a stumbling block ...

Thanks..

2. ### John PopelishGuest

Here is the not exactly right approximate run through.

There are two PN junctions in a transistor, one is the emitter to base
junction and one is the base to collector junction. Normally, the
base to collector junction is reverse biased, to produce an insulating
layer between the base and collector with no movable charges.

Lets pick a polarity... NPN.

So the collector has a positive voltage with respect to the base, so
the doped in electrons in the collector N material are attracted away
from the base and the holes in the base are attracted away from the
collector, leaving just insulating silicon between them.

When the base emitter junction is slightly forward biased (emitter
relatively more negative and base relative more positive), the doped
in electrons in the emitter are repelled toward the base, and the
holes doped into the base are repelled toward the emitter. At about a
half volt forward bias, the holes and electrons begin to find each
other and the electrons tend to jump into the holes and both
effectively dissappear. However, a well made transistor has the
emitter much more highly doped than the base, so more electrons get
pushed into the base than holes get pushed into the emitter.

So the holes that get pushed into the emitter are anihilated very
quickly, but the electrons that get pushed into the base have to hunt
around a while beforo they dissappear.

The small positive base voltage causes these electrons to wander
toward the base lead (the most positive voltage around them). But the
base layer is very thin, and the electrons drift rather slowly in that
direction. If the temperature was very low, this is about all that
would happen, and the forward biased base emitter junction would have
almost no effect on the collector curret.

But at normal ambient temperatures (well above absolute zero) the
movement of the electrons is randomized by the thermal energy in the
silicon, so they stagger quite randomly, with only a little progress
toward the base lead. And since the base layer is so thin, most of
them will never make it to the base lead. They will fall off the
cliff into the highly stressed charge-empty reverse biased base
collactor junction. There, instead of wandering in a drunken stagger
through a very small electric field (volts per meter) they will whoosh
out of the reverse biased junction, because it is much more highy
stressed with e-field. They become collector current.

The more strongly you forward bias the base emitter junction, the more
electrons are pushed into the base layer, and the more stagger over
the cliff into the collector, though there will also be more that make
it out the base lead. Over a wide range of collector current, the
collector be a fairly fixed multiple of the base current. This is the
transistor's current gain or beta.

So the electrons are drunks being encouraged with a slightly tilted
sidewalk onto a slightly down hill, vibrating curb, next to street
that tilts away from the curb, very steeply. Most never make it to
the end of the curb, but fall onto the street where they slide into
traffic.

This is the drunken bum on a crazy street transistor analogy.

3. ### Abstract DissonanceGuest

I have the same problem to some degree.

I have two suggestions that might help though.

Learn the 3 common mode configurations and play around with them to get a
good understanding of how to use them. You don't necessarily need to know
the inner workings of a transistor if you want to use them(although it can't
hurt). This will help you in recognizing the basic building blocks of larger
circuits that use transistors.

Learn the basic models and apply them to pratical, but small circuits. This
will/should help you in analyzing transistor circuits and also to make your
own.

For me, the fundamental problem comes from not understanding completely the
inner workings of a diode. A transistor, after all, is basicaly a diode that
can be controlled(like a vacuum tude) by a current. So if you can't
understand a diode then you can't really understand a transistor(atleast on
the fundamental atomic level).

I do understand the motion of electron flow and holes in a semiconductor and
also the junction as these are basic physics... but theres something more
that I can't seem to grasp.

My problem is that I insist on viewing it in terms of electron flow instead
of electrons and holes... I feel the hole idea is just a "trick"(even though
its equivilent it should work without it). But when I try to think about it
with just electrons I get the fact that electrons can move either way so the
diode has no problems conducting one way or the other(which is true but its
not symmetric). (its also true that the electrons will flow easily in both
directions at some point).

I can't figure out why for low voltages the current flow is more in one
direction than the other except that it has something to do with the
junction and electrons on one side not having enough energy to get over the
junction barrier(but they are able to get over it in the reverse direction
easily for some reason).

Anyways, to use a diode you don't have to understand its inner workings
either.

The idea with a transistor is that its like a pipe:

|
--------| | |---------
| | |
--------| | |---------
|

where the line inbetween is some "value" that controlls the flow from one
side to the other(could be water, light, etc...).

the left and right sides are the N junctions and the "value" is the P
junction(for NPN)... by attaching a voltage to the P junction you can remove
its effects(because after all it will resist flow but if you can remove it
then electrons will flow very easily).

If you think about it somewhat you can see that the P junction acts like a
barrier(just like a diode in a diode) but that since you have an N on the
other side the electrons have to flow through the P to get to it... by
controlling the effective "size" of the P region you can control how many
electrons flow(its like a variable resister to some degree).

Obviously if you had no P region between the two N's then electrons would
flow unimpeaded. The larger the region(corresponding to a larger distance
in a vacuum tube) makes it harder and harder for the electrons to get
across(meaning you have to have a larger voltage). By biasing the P-N
region properly you can weaken its effects and make it much easier for the
electrons to get across it. Hence you can use it as an "amplifier" by
putting a small varying single on the "valve" and having a large current
flowing through it.

There are other ways to use the transistors too but thats the basic idea for
the transistor amplifier. I think it mainly rests on understanding a diode
as its just two diodes(but different dopings) stuck back to back.

It would be nice if someone who really understood this stuff(and not just
that they think they do but actually do) would make some animations(or even
some simulations) of the inner workings. (I've seen some on the net but they
just tend to be crap and expect you to assume a lot of stuff without telling
you why).

Jon

4. ### David L. JonesGuest

Try this animated description:
http://www.lucent.com/minds/transistor/tech.html

http://en.wikipedia.org/wiki/Transistor

Keep trying until you find a description that clicks!

Dave

5. ### Jonathan KirwanGuest

The animations I've seen are 'crap'.

By the way, a place where I'm unsure is the idea of mobility of holes
as compared to the mobility of electrons in an N-doped material, for
example. (Not a diode, not a transistor.)

I believe I understand enough of valence for both the lattice atoms as
well as the dopant atoms, the lattice conduction band, the proximity
of the dopant's valance to the lattice's conduction band and the ease
with which room temperature thermal agitation can move n-dopant
electrons into the lattice conduction band, etc. All this seems
sensible.

But I see the mobility of both holes and electrons described as
different in the same material -- for example, in lower dopant
situations where the mobility is limited by lattice collisions, the
holes are about 3 times "slower" than electrons in a silicon lattice.
This is where I am unsure about the exact explanation.

Almost all the holes are dopant holes, where the thermal agitation is
enough to overcome the very slight eV required (30-50 milli-eV?) When
an electron in the conduction band does collide after being drift
accelerated by an E-field, it will most likely collide with a lattice
atom. The collision energy may be absorbed via an energy band
transition of one of that atom's electrons or else converted into
phonon energy in the lattice and energy in the electron as it leaves
again in a random direction. I don't suppose this necessarily often
creates another conduction band electron and a lattice hole atom,
though. And the only way a dopant hole "moves" is with recombination
events, where a conduction band electron is recaptured for a moment?

So is it correct to see that the reason for the difference between the
speed of electron motion and hole motion is due to the difference in
these mechanisms -- that of the mean free path and the E-field
acceleration for electrons and that of the frequency of recombination
events for hole motion?

Or?

Jon

6. ### Joe McElvenneyGuest

Andrew,
You are not alone!

Try this, it is much closer to the truth although, as with most
explanations, an over-simplification.

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

The base and emitter form a diode.

Put a forward voltage across that diode and electrons will flow
out of the emitter into the base (i.e. in a NPN transistor).

Now the base region is narrow and the base/collector junction is
biased so as to attract electrons to it.

So, on the way to the base terminal, more than 90% of them are
kidnapped by the collector and never get there. It acts like a
narrow pipe with a big hole in it.

More voltage on the base, more emitter current and so more of it
available to be diverted.

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

There are two hang-ups that can cause confusion -

1). Current flow in the collector is caused by a smaller current
flow in the base.

But what causes that base current in the first place? It is of
course the base to emitter voltage.

Essentially then, a transistor is a voltage (not a current)
operated device although when working out biasing, it is
convenient to stay with the 'current' model.

2). The collector-base region is reverse-biased.

Yes it is, but only for electrons trying to flow in from the
collector. For the electrons in the base trying to get into the
collector it is forward-biased.

Cheers - Joe

7. ### Guest

Dear friends,

Once again, the "VICE" issue has reared its head
("voltage-current/chicken-egg" or "voltage-current/cause-effect" to
some folks). When motors, generators, transformers, LED's incandescent
light bulbs, transistors, etc. are under examination, the VICE monster
often shows up.
In a bjt, the base current Ib, and the base-emitter voltage Vbe,
**mutually coexist**. They are interdependent, interactive,
concurrent, mutual, simultaneous, inclusive, joined at the hip, etc.
In other words one cannot exist without the other, but at the same
time, one is not "caused" by the other. Vbe does NOT "cause" Ib, and
vice-versa. Examine the I-V curve of any p-n junction, whether it be a
juction diode, gate-cathode terminals of an SCR, base-emitter junction
of a bjt, LED, etc., and it is immediately obvious that the curve
passes through the origin and does not touch either axis elsewhere. In
other words, diode current Id is zero only when diode voltage Vd is
zero, and vice-versa. If one is non-zero, so is the other.
In spite of this, some have insisted, since day one, that current is
"caused" by voltage. If that were the case (it isn't), then every
electrical device in the universe would be "voltage operated" and
nothing would be "current operated". We wouldn't even have to bother
with these terms.
A bjt is a *charge* operated device. Charge must be injected into
the forward biased b-e jcn, and the reverse biased c-b jcn. It takes
energy, or work in order to move the charge. Voltage doesn't move the
charge, energy does. Likewise with FETs. It takes energy, or work, to
charge the gate to source terminals.
With FETs, this charge and energy can be provided by either a
low-impedance constant-voltage source, or a high impedance
constant-current source. To keep it brief, a low-Z constant voltage
source is better suited for driving a FET gate due to the high-Z of the
gate. The v-source provides both Vgs and Ig, both necessary for FET
operation.
With a bjt, Ib and Vbe are also both needed for operation. A low-Z
constant voltage source, or a high-Z constant-current source could
provide both Vbe and Ib. Again, for brevity, a high-Z constant-current
source is better suited for driving the b-e junction due to its low-Z
characteristic and temperature dependency of current. The constant
i-source provides both Ib and Vbe, both of which are absolutely
indispensable.
All electrical devices require BOTH I and V working together in
tandem in order to function. Some devices, depending on their terminal
characteristics regarding impedance, temperature, etc., are more
amenable to being driven by a constant I source vs. a constant V
source, or vice versa. The constant I source provides BOTH I and V, as
does a constant V source. Have I explained myself? Best regards.

Claude

8. ### Abstract DissonanceGuest

yeah. To me too... I think
Do you mean holes in a p doped material as compared to electrons in a n
doped material?

I'm not entirely sure but what I think is the free(conduction/valences)
electrons have enough energy to "ride" the lattice in the sense that they
will not collide with any atom(in the sense as far as electrons and atoms
"collide").

If, say, one free electron "colides" with a bound electron then atleast one
must stay and the other must leave. I suppose the electron either doesn't
have enough energy to dislodge a bound electron, has enough only to exchange
places(which, as far as were concerned doesn't do much), or has enough to
dislodege a bound electron and not take its place(i.e. the avalanche
effect).

The hole concept though is really just a mathematical analogy of how bound
electrons move through the lattice. I would expect that conduction electrons
and holes are different but I have nothing to back it up. I suppose these
are the things you learn in an advanced class in semiconductor theory.

My guess is though that conduction electrons don't get captured in any real
size... even if they do it is a very smooth transition and for all pratical
purposes we can consider them as "free"(i.e., they don't take part in any
interactions on the lattice). I'm not sure how true this is or how well it
models the actual problem. I suppose it is determined by how strongly bound
the valence electrons are to the atom and the probability of an electron
getting "close" enough to an atom to be associated with it.

Now hole movement may actually be the exact same thing in the sense that in
a p doped material an "absense" of an electron(which basicaly means a
potential to bind the electron into its atom). The reason is we have to know
how strong the "hole" is. When an electron moves through a p doped material
depending on how stronge the holes affinity for the electron is it may be
completely captured by the atom(ofcourse this doesn't happen completely
but). If the holes affinity to capture the electron is very small then
obviously the electron acts like a free electron similar to in n doped
material.

heh, I have no idea. I doubt anyone really does and these are just models
we use that seems to work. Its surely a much more complex situation than
think about electrons floating around in a well defined lattice, etc...

I suppose its up to you to dig deep enough until you are satisfied with it.

I think what I said above basicaly boils down to saying that the difference
in speed due to hole flow and that due to free electron flow is due to the
hole affinity for the electrons. applying a potential across both types of
materials should result in the same mean free velocity if the atoms were
exactly the same(obviously). Hence the difference must come about from the
doping. N doping, AFAIK, is in effect lowering the free electrons
attraction from the lattice atoms... p doping will have the opposite effect
though.

You might think about it like and see if it makes any sense. Think of an
electron in an n-doped material moving along through space. As it
approaches an impurity there is a small repulsion due to the electron cloud
in the atom. We could graph the repulsion with time/distance as sorta a
convex parabola with maximum corresponding to the atom's nucleus(basicaly).

The "holes" are opposite as when the electron approaches an impurity in a
p-doped material there is an attraction and it gets stronger as the electron
gets closer corresponding to a similar, but concave, parabola(ofcourse not a
real parabola but just an approximation).

As the electrons bounce around in the p doped material there will be
attractions toward the valence shells of the impurity atoms.... but ofcourse
since the valence shell is full(or empty) this electron either cannot be
captured or will have to boot out another electron.

I have no idea how to tell though as it is impossible to fine what an atom
is and what it means to be "captured"(one would probably try and define in
terms of distance but thats only a mathematical concept).

I don't know and don't remember enough about nuclear physics to know whats
really going on though. You could bet that its you'll never arrive at the
answer though ;/ It sounds like you got the basic idea as far as I'm
concerned

For me, the real issue, and the more problematic is at the junction of two
oppositely doped materials. There seems to be some "strange" things
happening there. There has to be some non-symmetric aspect of this junction
IMO to give rise to its non-symmetric behavior. Most will use the hole
analogy to get the result but if you replace the holes with its
"corresponding" electron flow then it gets much more difficult as electrons
can "easily" flow in both directions.

What I have come up with in trying to understand it is that one gets two
charge density functions for the two biasing types.

One looks like this

/\ /\ |
/ \---/ \| --- /
|\ / \ /
| \/ \/

/\ | /\
---/ \| ---/ \
\ / \ /
\/ \/

where the | represents the junction and the "bumps" are the
potential/charage distribution.

The first one corresponds to a P-N that is reversed biased and the second to
one that is forward biased. As "pressure"(i.e., potential) is applied to
the second the far edge potentials get pushed closer to the center and
eventually will cancel out leaving a constant potential(approximately) which
means electrons flow easily through.

The first will just tend to increase the overall potential as more and more
voltage is put across it.

I'm not sure if this is the right interpretation but I basicaly got it as
thinking about how electrons would distribute themselfs in the two different
materials and by considering the junction potential.

The problem is that you can view it in two ways in that if you apply enough
"reverse" bias then electron flow will become easy too(you end up pulling
the two potentials apart so much that they become negligible...) this
correseponds to breakdown of the diode.

So the problem is not so much about symmetric as it is symmetric to some
degree but about magnituide. If you look at a diodes IV curn it is actually
pretty damn symmetric except the reverse current is scaled differently.

The reason is that it might just be harder for "hole" flow than conduction
flow and hence this makes it easier for electrons to flow in one way than
the other... but this isn't right either as it breaks physical symmetry
laws(flipping the material shouldn't change its behavior).

I'm still searching for what is really going on too ;/ Maybe one day it will
make sense.
Jon

9. ### ehsjrGuest

Why are transistors so extremely important? Because
there are millions upon millions upon millions upon
millions etc in use. The number is so huge its beyond
counting. They are used in almost every electronic
device most people encounter on a daily basis, throughout
the day.

Regrading the above, the confusion may come from pondering
"how it works" versus thinking about "what it does".
How it works gets into physics - how material behaves
at the atomic level. It's fascinating and interesting etc -
but not needed to understand *what* a transistor does.

So, look at what a transistor does.

It can be used as a switch that turns things on or off.
It can be used as an amplifier.

In both cases a small electrical source controls
the transistor at its input. And in both cases, the
transistor output controls a separate and much stronger
electrical source.

Damn clever engineers create a wide variety of circuits
that use these two functions of a transistor to do miraculous
things - display your heartbeat on an EKG machine, guide
rockets to the moon, control your microwave oven, create
an ABS system to prevent brake lockup on your car, allow
you to play games or surf the internet on your PC and
on and on and on.

All based on a device that is controlled by a very weak
source, which in turn controls a separate and much stronger
source. Yes, it is important!

Ed

10. ### Abstract DissonanceGuest

So your saying without a voltage(difference) the charge would still move?

Um.. Voltage is defined as the change in potential energy between two points
needed to move a "test" charge in an electric field between two points.

Hence it has everything to do with motion. One can argue that there is no
potential difference between two points unless an electron is moving.

If an electron is moving in an electric field then it is doing so because
there is a potential difference.

there are three explicit points involved in the definition: Distance,
charge, and the electric field. Since current measures the rate of change
of w.r.t to time past some point and since the speed of charge in a
conductor is approximately constant then current approximately measures the
amount of charge passing through a point at any given time.

If we consider a uniform electric field, say between two points a distance d
apart and electrons are flowing between the two points with a constant
velocity then

V = -q*E*d
and

I = a*q

hence

V = I*E*d/a

or if since E,d,a are all constants in this problem we see that V is
proportional to I.

i.e., ohms law in an ideal resistor.

in a transistor its the same thing except E and q are changing due(and they
are related).

But defintely there is a relationship and you can't have one without the
other. Voltage and energy are synonymous in the sense that you can't really
have a potential difference without moving a charge. When you measure a
voltage with your voltmeter you are actually measuring current flow on an
extremly small scale and for all pratical purposes you assume there is no
current flow.

Its true though that you can't have voltage without current flow but the
opposite is true too.
Yeah. I think you just need to understand that ultimately voltage and energy
related. They are exactly related by

V = U/q where U is the change in potential energy and q is charge.

Otherwise everything else seems to make sense(which you happen to point).
Just seems that you are implying in some cases that you can have current
without a voltage.

I think ultimately current and voltage are one in the *same* but we view
them from different perspectives. You can't have one without the other and
there is a relationship between them. This relationship is sorta a
transformation that depends on the physical constraints we impose on the
electrons... they are related by an electric field and in some sense they
the same manifestations of some singular phenomena. (sorta like the wave
particle duality idea or special theory of relativity or even how the
electric and magnetic fields are manifestations of the same thing(and are
equivilent in some sense depending on your "perspective"))

Anyways,
Jon

11. ### redbellyGuest

John,

I've seen quite a few descriptions of transistors, but this one has
given me a better feel for what's going on than any of the others.
(And I'm no slouch when it comes to math & physics.) Thank you.

Mark

12. ### redbellyGuest

That's the kind of thinking that finally allowed me to understand
photodiodes. Forget about electrons, holes, and bandgaps, and just
think in terms of current and voltage characteristics. (Still working
on my understanding of transistors.)

Mark

13. ### John PopelishGuest

I'm glad it helped you. That makes the effort worthwhile. I like
this story, because it can be extended to cover so many different cases.

It covers the case of collector to base low reverse and even forward
bias. The street is only slightly tilted, so some of the bums stagger
back up on the curb, or the street is a little higher than the curb,
so bums from the other side show up on the curb.

It also covers base thinning (curb narrowing) from increased collector
to base reverse voltage (Early effect). A narrower curb decreases the
chance that any bum will make it to the end of the curb, so the
current gain goes up slightly.

But mainly, the first part of the description illustrates that
junction transistors are thermal devices. Without the random drift
produced by heat, there is no collector current or current gain.

14. ### Dorian McIntireGuest

While I don't completely agree with Claude's post I can shed some light on
one concept you took issue with; the idea of a charge moving with no applied
voltage. It is indeed possible for a charge to move with no voltage.
Superconductivity is one situation where charges move with no applied
voltage. Granted, a voltage is initially required to get the charges moving
but the voltage is not required to keep charges moving at a constant rate in
a superconducting material.

One special case of this is an electron moving at some constant velocity in
a vacuum. Voltage is initially required to accelerate the electron but
momentum will carry it on at a constant velocity if no extraneous fields are
allowed to act on the charge.

This may seem to be minor point to some, but physical concepts such as
momentum, inertia and energy are just as important in electronics as they
are in mechanical systems.

Dorian

15. ### Jonathan KirwanGuest

I suspect this is not so good phrasing, as it might imply a dU divided
by some finite q. In which case, the result would be a dV, not a V.

I prefer to think of V, especially when using the word "change" in
phrasing, as the infinitesimal form: V = dU/dq (joules/coulomb) or
else just dU = V*dq = dV*q. Otherwise, if U and q are both finite,
they represent some meaningful average finite value or the differences
between two meaningful finite values, which is too often less "exact"
in my mind.

Jon

16. ### Joe McElvenneyGuest

I trust you feel better now

Cheers - Joe

17. ### Abstract DissonanceGuest

Technically if there is an electric field then there is charge moving then
there is work being done. Obviously there are electrons "moving" all the
time without a "field"(well, theres always a field though) but we don't
consider a voltage moving them. The reason, Ig uess, is that there is no
mean free movement and/or the voltages are extremely small as to be
inconsequential.

About the SC material. The problem with that is that one cannot do any work
with it(hence no voltage) else one has a perpetual motion device. If you
try to measure the current flowing the electrons will stop flowing(or
decrease depending on how much work was used to get them to move). Its
similar to the uncertainty principle. So we can only talk about it in a
theoretical way.
Yes, but you are forgetting that voltage is basicaly the work/energy
supplied or given up by the moving charge. The electron has energy(you said
momentum) so technically it has a voltage. Voltage is an abstract definition
as is an electric field. As far as nature is concerned theres no such thing
as a E field or voltage. So you say that when we apply a voltage to
accelerate an electron and then remove that voltage it is gone... but it is
not. We have just transfered it to the electron(as far as you can transfer
voltage(really transfering energy)).

I think the problem is that you are thinking of voltage in macroscopic terms
then applying it to the microscopic. (sorta like wave-particle duality).
I.e., if you could just look at one electron at the microscopic level then
you wouldn't be able to see a "voltage" directly. If you were watching the
electron and you saw it move then you could hypothesize that there was a
voltage applied to it by some electric field. But you wouldn't be able to
really "see" the voltage.

Basicaly these are mathematical concepts applied to natural so we have to be
careful what we really been by these ideas. Although I can see what you
mean when we "apply" a voltage then stop "applying" it but you have to ask
yourself "What does it really mean to "apply" a voltage?". Then you might
realize that a voltage is really looking at the boundry conditions of some
even... i.e., measuring the energy at one point in time then at another
point in time and if they are different then something must have
happened(i.e., a "voltage").

For an analogy I could create a "field" that discribes how people move. We
could think of people as point charges and then plot there velecity vectors.
We would see areas in the field that look like there are "paths"(like a
highway with all the cars going in one direction or in an elevator,
etc...)... We could then hypothesize there is some force that makes the
"people" go in that common direction. In some locations it would be
disorganized or random and we could say there is no field there. We could
come up with some way to measure this "field" and create a whole theory
around it. In actuality there is probably not a field though and it is just
a "tool"/"concept" used to help us understand why the people seem to be
moving as they do. We could say "These people over here are experiencing a
force that makes them move along this path" and "These people here have some
forces that are holding them together"(such as at a football game), etc...

Hell, who knows Basicaly the definition of voltage is independent of
what happens between two measurements so we can't really talk about what is
going between them(just like a particle as voltage is a measurement on
particles)... If we do talk about them we end up arriving at the problems we
do.

True, but they are not well defined physical terms. They are mathematical
concepts applied to reality. Any time you start to dive into this stuff all
kinds of little problems start creeping up and then you have to start using
the quantum mechanical definition of these terms to get around these
problems... but then even stranger things start happening. I do agree that
it helps and is usually a good idea but you gotta be careful in how you use
them too. Our knowledge about reality is very limited and is only decent
approximation. We could actually be way off and just by happenstance happen
to have a model that approximates it well. That is, our model's axioms could
be completely wrong in that the "real" model has totally different axioms
but it turns out that the end results(large theorems) happen to agree with
each other. I have a feeling this is what is going on and our concepts of
reality is way off(but in some sense parallel to reality). This is why we
have so many little problems in the sciences today that don't make much
sense and it seems that we keep on having to modify them to get it to work
and introduce things that make less and less sense. I doubt thats how
reality works but it could be. My evidence is it seems everyone we find a
problem in nuclear physics it seems we have to create/find a new particle to
make everything right again... It could be this way or we are just "forcing"
it to work.

Anyways,

Jon

18. ### Abstract DissonanceGuest

But thats what it is depending on how you look at it

It doesn't matter to much if you use a dV or V as long as you are
consistant.

Why? in either case you arrive at the same result and also V is really a
difference in itself(but on a global scale). They are really relative terms
and we tend to use concepts like dV -> ^v(delta V) -> V -> limit V->oo to
move through the different "resolutions".

I do see what you mean. Normally it should be written xV = xU/q where x
represents the "resolution". But since we normally take V to have 0
reference at infinity it doesn't matter in the end result.

Cause with your logic one could even say that q should be dq and we must
write dV = dU/dq but it depends on how we are treaing q. i.e., if q =
int(dq). if dq is not changing with position or time then we would normally
write q but if we are setting up an equation to handle varying q we have to
write dq and integrate).

I guess what I mean is that dV = dU/dq implies that we are dealing with
infintesimal quantities that will be used as part of a larger picture(i.e.
to integrate over). But if we are only dealing with "point charges" then we
can think of dq as = q and write a "simplified" notion of dV = dU/q. Now
since U and V does not depend on the path taken we can write it as Va - Vb =
(Ua - Ub)/q which in the standard notation delta(V) = delta(U)/q. But if our
reference point for V is taken to be Vb = 0 then we have either Va =
delta(U)/q or Va = U/q depending on how we look at it. delta(U) means change
in energy and U means change in energy w.r.t to an infinit point.

So you end up getting the same result since Va = Va - Voo. i.e., the
potential difference ALWAYS represents a "change" as does the potential
energy. So while notationally it might be a bit confusioning in general we
take a "short" cut to have to write one or two less characters as long as we
know that we mean that they represent differences else they make no sense.

so you can write it as dV = dU/q, V = dU/q delta(V) = delta(U)/q or V =
delta(U)/q. If you want to be precise depending on the problem then ofcourse
you have to choose the appropriate notation. (i.e., if you are dealing
writing a differential equation for the problem to find out is macroscopic
characteristics then you need to use the dV = dU/dq version).

heh. I guess what I'm saying is that its true if we use dU then we need to
use dV. In actuallity the real difference is simply that its always dV (or
delta(U) and delta(V)) because there is no such thing as V... but we
interpret V to be V - V_oo and make V_oo = 0 so we are left with just V....
so even though if we use delta(V) it is always equal to V with the above
criteria.

So mathematically you are correct but since we have that little criterion it
makes it *ok* for basic use.

i.e., when you measure voltage you are actually measuring between two
points... but we almost always use gnd as an implicit reference so we can
talk about the potential at a point(w.r.t to ground implied). I don't see
it as being technically wrong if everyone is in agreement about the implicit
reference used.

yeah, but if V = dU/dq then mathematically it makes no sense if V is implied
to be a real number. dU/dq are not real numbers(or even complex) so we can't
get a real number from there ratio. Hell, differentials themselfs are not
really mathematically sound anyways and really are just short cut(as most
mathematics is anyways) to writing difference equations and then taking the
limit. As long as you are consistant in what you mean then it should be
ok... after all, they are just symbols anyways and they could mean anything
you want them to. (Ofcourse mathematicians have defined standard meanings
for them so everyone can communicate easily)

Jon

19. ### Jonathan KirwanGuest

No, I couldn't logically say that for a physical system of finite
functions of U and q.

Jon

20. ### Abstract DissonanceGuest

What do you mean by finite functions? Discrete functions? bounded functions?

If you mean that q can only take on discrete values(and even U) then you can
say it pretty easy. Differentials exist for all for generalized functions
which can be used to sorta make discrete functions act like continuous
functions(I mean that mathematically you can use the same notation and
theorems).

i.e, say you have 10 point charges you can make this function into a
"normal" function(I mean one that behaves in mathematically similar way to
normal functions that you see every day) by using dirac delta functions. You
can then integrate and differentiate this function just like "normal"
functions and arrive at valid results just like normal functions.

You have to remember that this is mainly all notation and depending on what
concept you attach to the notation could make it "mean" something completely
different.

If you want to know what I mean just look up stieltjes integrals and it has
a pretty clear idea of what I mean. Basicaly lets you integrate over a
discontinuous
"differential"(notationally anyways).

Ultimately in the standard definition derivatives you are right but
physicists always try and bend the rules to make things easier to work with
so one has all kinds of extentions of notations and theorems that ordinarly
would seem odd to most people.

for example, check out fractional differentiation/calculus. You will seed a
notation that looks like an ordinary derivative but instead of the "nth"
derivative its something like the "rth" derivative where r is not an
integer. You could call it an abuse of notation but really its just an
extension made by someone that fits logically into the frame work in most
cases and sometimes can even be helpful.

Jon