# What should be the independent variable in a resistance experiment?

I was asked a question by a student today and I have been pondering about it for a while now. In an experiment to measure resistance of a conductor, should we vary voltage across the conductor and measure the current or should we vary current flowing in the conductor and measure voltage across it?

Experimentally, which would give us better results?

I've been thinking that in either case the drop across the ammeter or voltmeter should be very little (and almost of the same order). So would it make any difference?

• You need to be careful because a good conductor will have less resistance than your ammeter! One method that may work is to have a very precise voltmeter and measure the voltage drop across the ammeter as well as the conductor. – PhysicsDave Apr 29 at 20:56
• I wonder if it should be fix the voltage across (or current through) the conductor rather than vary. It's not a big deal but if you vary, say, the voltage across and then measure the change in current through, you're can calculate the dynamic resistance $r = \frac{\Delta V}{\Delta I}$. If instead you fix the voltage across to some non-zero value and then measure the current through, you can calculate the static resistance $R = \frac{V}{I}$. In either case, the voltage across is the controlled variable. – Alfred Centauri Apr 29 at 22:18
• What's wrong with using an ohmmeter to measure the resistance? – David White Apr 30 at 0:11

In principle it doesn't matter so long as you measure both the voltage and the current accurately (don't just trust that the value of the independent parameter is whatever you set the source to). You ideally want to use Kelvin sense connections to be able to measure the two operating parameters independently.

You also usually want to avoid applying a voltage or current that will cause significant self-heating which might alter the properties of the resistor being tested.

For low-value resistors (below 1 $$\rm \Omega$$) it's usually more convenient to use a fixed current source and for high-value resistors (above maybe 10 $$\rm M\Omega$$) we most often use a fixed voltage source.

• The Photon, would you mind adding a bit to the last paragraph explaining why it's more convenient? – Alfred Centauri Apr 29 at 22:19

In addition to what @The Photon has suggested, have you considered using a Wheatstone Bridge? Although it is an old method and digital multimeters provide a simple way to measure resistance, a Wheatstone Bridge can be used to measure very low values of resistances in the milli-ohms range. Whether or not it is useful will depend on the conductor, its gauge, and its length you are measuring.

For example, an 18 AWG copper conductor has a resistance of about 6 ohms per 1000 feet depending on the grade, or about 6 milli-ohms per foot.

The accuracy of the Wheatstone Bridge will, of course, depend on the accuracy of the 4 resistors used to balance the bridge.

Hope this helps.