AA battery as Thevenin not Norton - RF Cafe Forums
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Post subject: AA battery as Thevenin not Norton
Unread postPosted: Tue Dec 28, 2004 8:33
Why AA battery represented as Thevenin instead of Norton?
Unread postPosted: Wed Jan 05, 2005 7:55 am
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 ohm.
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
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!
Unread postPosted: 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.
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.
Keep up the great work!
Unread postPosted: Mon Jan 10, 2005 8:33 am
Joined: Mon Jan
10, 2005 7:13 am
Location: the Netherlands
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 all!
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
Now, you demnstrate before your class that:
- the open circuit voltage is equal
short circuit current is the same
- the voltage and current with any load, even an artifially made negative
resistance is equal
proving that 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. :wink: