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Re: voltages etc.



Seth T Miller wrote:

Part One: Take a 6 volt dry cell battery. My colleague opines that
one cannot speak rightly of a voltage existing between the two sides
of the battery until the terminals are connected, thus completing the
circuit. Her reasoning is that the chemical reaction is the source of
the voltage and does not occur unless the terminals are connected in
a circuit (except perhaps in very small amounts as batteries run down
when left to stand).

Wow.

Is this a correct analysis

No. It's pretty much as wrong as it could
possibly be.

> or can we rightfully speak of a voltage
difference between the two sides of a battery, and if so is it 6
volts in this case?

First, a slight digression:

In situations like this, getting the physics right is
easy compared to getting the pedagogy right. The
customer is obviously laboring under some misconceptions
about the physics or the terminology (or most likely
both). The trick is to figure out where she's coming
from. This is exceedingly hard to do by email; if
I were there in person I would ask a bunch of questions
(what's the definition of voltage?) to figure out what
are the underlying misconceptions.

After consulting a crystal ball or two, and making use
of some hints from her question 2 (below) I'm going to
guess that the customer is confused about what happens
to "the" voltage in an open circuit. There is a very
deep physical principle involved here, namely gauge
invariance.

Fact: a 6V battery just sitting there (not connected
to anything) has a 6V voltage difference between the
terminals. No chemical reaction takes place to
maintain this voltage. No chemical reaction is needed
to maintain the voltage ... unless and until you hook
up a circuit and start drawing current. The rate of
the chemical reaction is directly proportional to the
current. In fact for most of the history of electrical
science, the unit of charge (and hence current) was
_defined_ in terms of an electrochemical reaction. Some
guy named Faraday had something to say about this. No
current, no reaction.

Fact: when a 6V battery is just sitting there, you
don't know the voltage on either terminal. But you
know there is a 6V difference between them. This
sometimes gives non-experts the wiggins. I personally
have been comfortable with this idea since I was
about six years old, the idea that you could know
the difference between two numbers without knowing
either one separately, so it is a major struggle for
me to be patient with those who don't immediately
see it..... We are surrounded by things that have
this property. Suppose you have a meter stick
aligned east-west. Given just the stick, you don't
know the longitude of either end, but you know the
ends are 1m apart. Suppose you have a pendulum that
is just long enough to have a one-second period. Given
only the pendulum, you don't know the start-time of
the swing and you don't know the end-time of the swing,
but you know they are one second apart.

These are deep symmetries of nature. These are among
the deepest principles in all of physics.

So I suspect the customer is not sure whether she
is asking about "the" voltage on a given terminal or
about the voltage difference between terminals. One
question is unanswerable (for reasons having nothing
to do with chemistry) while the other question is
easily answerable.

Part Two: My colleague connected the positive side of a 6 volt dry
cell battery to a 1.5 volt light bulb, then connected the other side
of the light bulb to the ground. The bulb does not light. Is there a
voltage difference between the positive side of the battery and the
ground and if so is it 6 volts? Why doesn't the bulb light?

Probably the same bundle of fundamental misconceptions.

The very notion that there is any such thing as "ground"
is a non-gauge-invariant notion, and therefore highly
suspect.
a) You can choose any thing you like and call it
ground (by exercise of your gauge freedom) but don't
be surprised if others choose differently.
b) If you do a calculation and the prediction
depends on your choice of ground, the calculation is
wrong.

My crystal ball says that no matter what the customer
says about voltage _between_ the terminals, she is
actually thinking in terms of voltage "on" the terminals.

Electrical engineers like to draw schematics where
one side of the battery is hooked up to a "ground"
symbol and one side of the load is hooked up to a
"ground" symbol, with no discernible connection
between the "grounds". That is perfectly OK as
a medium of communication between people who know
what's going on, because they implicitly know that
all the "grounds" need to be hooked together with
real physical conductors. But neophytes commonly
think that the (-) terminal of the battery gets
connected to "ground" just by magic, requiring
nothing but wishful thinking. Well, sorry, that
kind of magic requires a lot more than wishful
thinking; you have to go off to Hogwarts and
study real hard for several years.

Her latest theory is that as soon as one touches the positive side of
the battery, any excess charges are immediately drained off and that
side of the battery becomes equalized with the ground. The chemical
reaction is not occurring, so there is no way for a voltage
difference between the positive terminal and the ground to be
maintained, thus the bulb does not light.

Actually, depending on how you look at things,
that part could be brought into contact with
real physics. The following analysis is not
suitable for customers at the introductory level,
but if non-swimmers want to jump into the deep
water, the story goes like this: You can analyze
the battery as a _three-terminal_ device: the
nominal (+) terminal, the nominal (-) terminal,
and a third terminal connected to whatever you
are calling "ground" and representing the stray
capacitance. The magnitude of this stray capacitance
is about a billion times smaller than the effective
capacitance (Q/V) of the battery, so it is
somewhere between academic and misleading to even
mention it. If you do mention it, you need to
use a very systematic notation so you are clear
about what currents and what voltages are seen
at which terminals; you can't just glibly talk
about "the" voltage on "the" battery.

At the introductory level, I would recommend
saying that the stray capacitance is negligible,
and saying that before connecting to either
terminal the absolute voltage was unknowable.
This is consistent with the level of approximation
embodied in Kirchhoff's laws -- neglect of stray
capacitance (and stray inductance et cetera).

Also at the introductory level I would frown
upon any mention of the word "ground".

========

Note that this confusion about "ground" makes
contact with the thread last week about birds
perching on high voltage wires.