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I have a power supply, multimeter, and a copper wire with cross sectional area (A) A= 2.14*10^-3 m^2, Length L = 0.13 m and the resistivity of copper is p=1.7 × 10-8. The goal is to find the resistance of my copper wire, but I'm not sure what other instruments I need to determine the resistance, or how to setup the circuit to find out the resistance. After using the resistance equation, I found that the resistance should be about 1*10^-6 (ohms), but I cant get close to that answer. How should the circuit be setup?

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    \$\begingroup\$ How much current can your power supply provide? Do you have a second multimeter, or does the power supply have an internal ammeter? What is the lowest voltage your multimeter can accurately measure? \$\endgroup\$ – The Photon Oct 6 '17 at 4:29
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    \$\begingroup\$ You are describing testing a piece of "wire" about the size of a soda can. Fix your figures first, or find a new piece of wire, more like 1 m long and 1 mm diameter, or 1x10^-6 m^2 area. It is possible to measure the resistivity of a piece of bulk copper, but you'd need hundreds of amps, and the calculations of the current flow are quite different to the simple formula. \$\endgroup\$ – tomnexus Oct 6 '17 at 5:53
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    \$\begingroup\$ @tomnexus He does not need any power supply. I think it is just a homework, and "power supply" in the question is supposed to distract students. \$\endgroup\$ – Chupacabras Oct 6 '17 at 6:05
  • \$\begingroup\$ Well, if the OP is trying to measaure 1 uOhm, it will be rather difficult, as tonnexus points out. Even 1000 A will only produce 1mV. \$\endgroup\$ – mkeith Oct 6 '17 at 6:28
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    \$\begingroup\$ Measuring the resistance of very small resistances, like a copper wire with a multimeter is unreliable. I suggest using a Thomson bridge, which gives much better accuracy at low resistance values. \$\endgroup\$ – Bart Oct 6 '17 at 8:58
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As MKEITH said, copper has a temperature coefficient; its 0.4%, or 4,000 ppm, per degree Centigrade.

Copper, as with other materials has a thermal timeconstant (or, when inverted, a parameter named thermal-diffusivity).

For a cubic meter of copper, the time constant is 9,600 seconds (about 3 hours).

For 10cm cube (4" on a side), the time constant is 100X faster or 96 seconds.

For 1cm cube, the time constant is another 100X faster, or 0.96 seconds.

For 1mm cube, Tau is another 100X faster, or 0.0096 seconds.

Thus measurement has be made extremely quickly, or the temperature rise must be very small.

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In general, you use a power supply to run a known current through the wire, and measure the voltage drop using a voltmeter accurate to the mV level. Then you use Ohm's law to calculate the resistance. V = I * R. V is the voltage on the voltmeter, I is the current, and R is what you want to know. You probe with the voltmeter at the exact location where you want to know the resistance.

Note, copper is a good conductor, but its conductivity is fairly sensitive to temperature. If you run so much current through it that it warms up, the resistance will change. So best to measure reasonably quickly, then disconnect the power.

Further reading: Four wire resistance measurement https://www.allaboutcircuits.com/textbook/direct-current/chpt-8/kelvin-resistance-measurement/

Copper resistance temperature coefficient http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html Basically, for every degree of temperature increase, the resistance increases by 0.4%. So if it is 1 Ohm at 25C, ti will be 1.004 Ohms at 26C, and so-on.

In this specific question, I have my doubts that the dimensions are correct. A cross section of 0.00214 m^2 would be a very large wire, around 52mm (2") in diameter. Measuring the resistance of such a wire would require a very large current to give rise to any appreciable voltage.

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In addition to my previous answer, there is a simpler way to calculate that resistance.
https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

\$ R= ρ \times \frac{l}{A} \$
\$ R= 1.7 \times 10^{-8} \Omega.m \times \frac{0.13 m}{0.00214 m^{2}} = 1.0327 \mu\Omega \$

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    \$\begingroup\$ That seems like a high resistance for round copper bar which is 5 cm in diameter and 17 cm long. \$\endgroup\$ – Andrew Morton Oct 6 '17 at 14:08
  • \$\begingroup\$ @AndrewMorton You are right, a missed one character. Fixed. Thanks for pointing out. \$\endgroup\$ – Chupacabras Oct 6 '17 at 17:12

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