From: Marc Kossover (zeke_kossover@yahoo.com)
Date: Tue Jan 11 2005 - 13:26:03 PST
Message-ID: <20050111212603.43190.qmail@web53404.mail.yahoo.com> Date: Tue, 11 Jan 2005 13:26:03 -0800 (PST) From: Marc Kossover <zeke_kossover@yahoo.com> Subject: Batteries and Electromagnets (was Practical Lab Questions)
--- Dylan Golden <dylngldn@lycos.com> wrote:
> 2) In making electromagnets and mini light bulb
> circuits we generally use 1-2 1.5V D cell batteries.
> How do 9V batteries and 1.5V AA batteries compare
> in terms of efficacy and longevity? The AA
> batteries are much cheaper than the D batteries.
> The 1.5V batteries are nice because they can be
> stacked.
Executive summary:
Stick with the D cells. They will give you the most
bang for the buck, and will probably give the best
magnetic field too.
Long Answer:
This is actually a surprisingly hard problem. The high
school level physics is pretty easy, but the physics
and chemistry of batteries is much harder.
The strength of the magnetic field of a solonoid (your
electromagnet) is related to the number of turns of
wire per unit of length and the amount of current in
the wire. How well you wound the electromagnet
determines the first term.
On the other hand, the amount of current running
through the solonoid is determined (as long as it is
DC) by the resistance of the circuit and the voltage,
following Ohm's Law, current = voltage / resistance.
For a pre-made electromagnet, you can't control the
length of the wire, and so you can't control the
resistance. (See a note below about electromagnets you
make yourself.)
On the other hand, you can control the voltage. More
voltage means more current, and more current means
more magnetism. Therefore, it would seem that using a
9V battery would be the way to go. In practice,
though, they work less well.
----The problem is a property of batteries called internal resistance. Imagine connecting a wire between the terminals of a battery. Since the wire has a very small resistance, one might think that the current would be enormous. In practice it isn't, though. Every battery has an internal resistance that adds to the resistance of the circuit and limits the current.
An average 1.5 V AA alkaline battery has an internal resistance of about 0.4 ohms, meaning that a typical alkaline can provide no more than 3.75 amps (1.5 V / 0.4 ohms) even if shorted, and probably less since most batteries' internal resistance increases as the they discharge. See <http://home.att.net/~mikemelni1/intres.html>
Most users don't notice somthing like internal resistance since the resistance of the load -- the things connected to the battery -- are much larger than the resistance of the battery. However, the resistance of an electromagnet is often on the same order as the resistance of the battery, and so it plays an important role.
Still, you might figure that you could stack batteries together in series to make a higher voltage. This works, since the voltages of each battery add, but so do the internal resistances.
For example, imagine a 1.5 V AA battery with an internal resistance of 0.4 ohms connected to an electromagnet with a resistance of 0.6 ohms. The total resistance is 1.0 ohm -- 0.6 ohms plus 0.4 ohms -- and the current in the circuit is 1.5 amps -- 1.5 V / 1 ohm.
Putting two 1.5 V batteries in series yields 3.0 V. The total resistance is 1.4 ohms -- 0.4 ohms + 0.4 ohms + 0.6 ohms -- and the total current is 2.1 amps -- 3.0 V / 1.4 ohms. More current, yes, but not twice as much.
Each additional battery has less and less effect. Four more batteries (six batteries total) in series give a current of only 3 amps.
And! Batteries in series all discharge together at somewhere close to the single battery by itself.
So, a pair of batteries in series is an improvement over a single battery, but the incremental returns rapidly diminish.
----
Why am I recommending a D cell over AA?
A battery has only so much energy stored in it. That is, each battery only has so much metal that can react. Once the chemistry is finished, the battery is dead.
Generally, larger batteries have more energy stored in them. The industry standard is to give the energy in milliamp hours -- so that a 2000 milliamp hour battery could supply 2 amps for 1 hour or 1 milliamp for 2000 hours -- although the chemistry usually prevents these kinds of extremes. A typical AA battery has 2800 milliAmp hours, while a D size battery might have seven times that amount. <http://data.energizer.com/SearchResult.aspx>
As long as D cells aren't seven times as much money, they are a better deal, and usually they are only twice as much.
----
How about 9 V?
Bad investment all around. First, 9 V actually consist of six small cells connected in series to make the 9 V. (Back in the bad old days, people called AAA, AA, C, and D batteries "cells" since they consisted of a single cell and 9 V and lattern batteries "batteries" since they consisted of a battery of individual cells.) Each one of the cells has a small capacity (625 mA hr) and the capacities are used up together since they are connected in series.
I don't know this for sure, but I suspect that 9 V have greater internal resistance which would mean less current for the magnetic field than with D's.
If you really want 9 volts, just connect six D cells in series.
-----
How about Lantern Batteries?
These consist of four large cells connected in series, about 26000 mA hr for an Energizer. They have the voltage of 4 D's connected in series, but only 25% more capacity (the D's capacities don't add since they are in series). They usually cost a lot more than four D cells, and the increased voltage isn't really that useful. Stick with D cells.
Marc "Zeke" Kossover The Jewish Community High School of the Bay
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