Post subject: AA battery as Thevenin not Norton
postPosted: Tue Dec 28, 2004 8:33 am
Why AA battery represented
as Thevenin instead of Norton?
Unread postPosted: Wed Jan 05, 2005 7:55
This is obvious: when you represent a battery as an ideal
voltage source with an internal resistor in series you get what you
actually have: when you measure its terminal voltage with a very high
resistance instrument you (almost) get the voltage of the (ideal) source,
when you short is, you get the short circuit current. when you repeat
these measurements some time later you get the same results.
However, when you represent it as an ideal current source with an internal
resistor in parallel you will find that at first your measurements agree
with the voltage source model, but after a finite time they don't: the
battery has run out.
Some figures: an AA battery has a terminal
voltage of 1.5 V, a short circuit current of about 10 A and a capacity
of about 1 Ah.
This means it has an internal resistance of 1.5/10=0.15
A voltage measurement on the Thevenin equivalent with a
standard 10Mohm DVM will yield 1,49999978 V. Even on a six-digit instrument
this will round to 1.50000 V.
This measurement can be repeated after
several years, and will give the same results, provided that the battery
is kept at a constant temperature.
If the battery is considered
to be its Norton equivalent, the 10A source will feed its current through
the 0.15 ohm resistor, giving -indeed- a terminal voltage of 1.50000
V. However, after 1/10 hour or 6 minutes, the battery will have run
out, so the experiment can not be repeated.
You can see, never
believe your teachers when they say that Thevenin and Norton are equivalent!
Wed Jan 05, 2005 9:13 am
Joined: Mon Sep 01, 2003 6:59 pm
:smt038 Your entire post is a great answer, I wish all responses
were this complete! Thanks for putting the effort into it.
You can see, never believe your teachers when
they say that Thevenin and Norton are equivalent!
While I realize
this is a tongue-in-cheek remark, in fact it is true that Norton and
Thevenin are equivalent if you are mindful of the ideal current/voltage
supplies used in the theoretical models, whereas the battery source
is not ideal and therefore favors one model over the other.
up the great work!
Unread postPosted: Mon Jan 10, 2005 8:33 am
Joined: Mon Jan 10, 2005 7:13 am
This is quite a compliment to get from dr. Maxwell
himself, or is his deamon speaking? However, after figuring out how
to sign this post, I have to comment. This is not tongue-in-cheek at
Suppose you have an ideal voltage source of
1 V and an ideal current source of 1 A (naturally the latter one is
carefully shorted). Let's say that you got them from an alien or that
you are only conducting a thought-experiment, but the sources are realy
IDEAL, including the fact that the sources are inexhaustable.
Now, to teach your pupils the Norton-Thevenin equivalency theorem,
you mount the voltage source in a black box, connect it to two external
terminals and insert a 1 ohm resistor in series with the voltage source.
You do the same thing with te current source, but there the 1 ohm resistor
is shorting the terminals.
Now, you demnstrate before your class
- the open circuit voltage is equal
- the short circuit
current is the same
- the voltage and current with any load, even
an artifially made negative resistance is equal
Norton and Thevenin are equivalent.
However, now a smart student
comes forward and proposes the following experiment: put both black
boxes (wit open terminals) in two equal reservoirs filled with an equal
amount of deionised water. Both reservoirs are prety good thermal insulators
and equipped with a thermometer.
When we observe temperature
over time in both devices, we will see that one of them is rising, while
the other one remains at room temperature.
It can easily be seen
that the device with the rising temperature contaisn the current source,
while this black box is dissipating 1W of power. Hence the other one
is te voltage source.
QED, Norton and Thevenin are NOT equivalent,
you can -evidently- device a thought-experiment that distinguishes them.