# AA battery as Thevenin not Norton - RF Cafe Forums

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Uncle Ezra

Post subject: AA battery as Thevenin not Norton

Unread postPosted: Tue Dec 28, 2004 8:33 am

Why AA battery represented as Thevenin instead of Norton?

Thanks

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Guest

Post subject:

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 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!

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maxwell

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Unread postPosted: Wed Jan 05, 2005 9:13 am

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Captain

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Joined: Mon Sep 01, 2003 6:59 pm

Posts: 13

Location: Boston

:smt038 Your entire post is a great answer, I wish all responses were this complete! Thanks for putting the effort into it.

Anonymous wrote:

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.

Keep up the great work!

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hugo

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Unread postPosted: Mon Jan 10, 2005 8:33 am

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Joined: Mon Jan 10, 2005 7:13 am

Posts: 1

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!

Proof:

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 that:

- 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

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:

Posted  11/12/2012