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My son is doing a science experiment on how varying temperature and diameter of wire impacts the resistance. We are assuming we can accomplish this by using different gauge wires, a home thermometer, and a basic digital multimeter (e.g. this one at amazon).

Is this correct, or is the multimeter only used to measure resistance of batteries and circuits and not a plain piece of wire? If this setup is not sufficient, can you suggest an alternative?

Regarding temperature, will a simple home thermometer (battery, not mercury) be sufficient?

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6 Answers

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Hmm your experiment sounds like a good idea but I think it'll be much harder than you're imagining. The resistance of wires is very low. After all, they are designed to conduct! Check out this table. 30 gage wire has a resistance of $0.1\: \Omega/\mathrm{ft}$ which is well below what a typical multimeter can read.

Also, because the resistance is so low, one very big source of error will be how well the multimeter probes are attached to the wire. You'll likely end up measuring the resistance at the point of contact as much as the resistance of the wire.

One way to help though is to measure very long wires. If you can get wire a few hundred feet long the resistance of the wire will start to be high enough that meaningful measurements can be made, despite experimental error.

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Instead of using a long coil of wire, would using one with a relatively high resistance like nichrome (used in heating elements) work as well? –  Dan Neely Dec 16 '13 at 19:34
    
@DanNeely: yes, nichrome should work well. –  Ross Millikan Dec 18 '13 at 0:18
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As others have noted, the big issue is getting the resistance of the wire into the range where your multimeter can measure it accurately. For that, the simple approach is to make the wires as long and thin as you can in order to maximize resistance.

That said, another thing you can do is improve the precision of your measurements, e.g. by using four-terminal sensing, a.k.a. Kelvin resistance measurement. For this, you'll need to pass a current through the wire and measure both the current and the voltage drop across it:

Kelvin (4-wire) resistance measurement
Image source: All About Circuits vol. I, chapter 8.9

This arrangement allows you to exclude any additional sources of resistance along the current path, such as the contacts between the voltage source terminals and the wire, from the resistance measurement. Note that, while the circuit shown above includes a separate voltmeter and ammeter, you could also replace the ammeter with a shunt resistor with a known resistance and measure the voltage across it, as in the circuits shown at the bottom of the page linked above. This would allow you to do the measurement using only a single voltmeter. As a bonus, the shunt resistor would also serve to limit the current across the circuit.

Warning: Never connect a voltage source, such as a battery or a simple lab power supply, directly across a low-resistance wire. This will create a short circuit, potentially causing the wire or the power supply to overheat. Instead, always include an appropriately sized resistor in series with the power supply to keep the current down to a reasonable level.

For an even more accurate resistance measurement, you could set up a bridge circuit, like the basic Wheatstone bridge shown here:

enter image description here
Image source: All About Circuits vol. I, chapter 8.10

Such circuits can allow very accurate resistance measurements by comparing the resistance to be measured with resistors of known values. In particular, for measuring low resistances, you might want to look at the Kelvin Double Bridge circuit described further down the linked page.

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Wire typically has very low resistance, so what you'll most likely end up measuring is the contact resistance.I.e., the resistance between your multimeter probes and the wire itself might have more resistance than your wire and overshadow it.

My suggestion for the temperature dependent part would be to measure the resistance of the wire with it in boiling water and ice water, for two easy reference points.

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Most tap water (ionized water) conducts electricity rather well. Could a hundred feet of coiled wire in boiling water introduce enough additional conductivity to be statistically significant for the experiment? –  Brandon Enright Dec 16 '13 at 6:43
    
@BrandonEnright for comparison: some time ago I made an experiment putting a 220V pair wire into salted tap water (in a 1 l cup) and looking at electrolysis. When I put a green LED into it, I saw it glow green - not even orange as would be in case of overcurrent. Of course, moving it closer to wires made glow orange. Now compare it with what I'd see if I connected the LED directly to the 220V wire. So I'd conclude that tap water is not significantly conductive compared to metal wire. –  Ruslan Dec 16 '13 at 8:48
    
@Ruslan the prongs on an LED are pretty close together. The fact that there was a $\sim 3\: \mathrm{V}$ potential across them in the water suggests that enough current is flowing through the water to throw off a precision test of the wire's resistance. –  Brandon Enright Dec 16 '13 at 8:50
    
@BrandonEnright: So use insulated wire? –  Ilmari Karonen Dec 16 '13 at 14:57
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I did a similar experiment this year for my final science assignment. We used a transformer which had two long coils of copper wire inside, of different lengths (10m and 750m) and thicknesses. Pop open the transformer and take out the coils. Set your multi meter to ohms and touch the contacts to either end of each of the coils (We got 2.2 ohms and 1500 phms respectively). Since the coils of wire in the transformer are insulated, you can then place the coils in freezing/boiling water with the ends sticking out. Measure the resistance now, and you should notice a difference.

We got our 1.5k ohm resistor up to 3k+ ohm just going from 25C to 100C.

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That is the correct process, but you will want a multimeter that reads down into the 0.1 $\Omega$ range, something the Amazon-linked multimeter cannot do.

Most home thermometers have a maximum of about 110 $^\circ$F, so if you plan on raising the temperature to larger than that, you'll want something different, something like this laser thermometer (Amazon link).

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A "candy thermometer" you can pick up at any grocery store will also go way above 110 F. It might not give the needed precision, but it's cheap and easy to get in a hurry. –  R.. Dec 16 '13 at 9:27
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Typically a wire with higher resistivity is used e.g. Constantan. Then see the experiment here.

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Hi Music Stu, link-only answers, especially ones directly to a PDF are frowned upon. Can you update your answer to include more details so that the PDF isn't strictly needed? –  Brandon Enright Dec 17 '13 at 23:59
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