4-wire resistance measurement
PARTS AND MATERIALS
It would be ideal in this experiment to have
two meters: one voltmeter and one ammeter. For experimenters
on a budget, this may not be possible. Whatever ammeter is
used should be capable measuring at least a few amps of
current. A 6-volt "lantern" battery essentially
short-circuited by a long piece of wire may produce currents
of this magnitude, and your ammeter needs to be capable of
measuring it without blowing a fuse or sustaining other
damage. Make sure the highest current range on the meter is
at least 5 amps!
CROSS-REFERENCES
Lessons In Electric Circuits, Volume
1, chapter 8: "DC Metering Circuits"
LEARNING OBJECTIVES
SCHEMATIC DIAGRAM
ILLUSTRATION
INSTRUCTIONS
Although this experiment is best performed
with two meters, and indeed is shown as such in the
schematic diagram and illustration, one multimeter is
sufficient.
Most ohmmeters operate on the principle of
applying a small voltage across an unknown resistance (Runknown)
and inferring resistance from the amount of current drawn by
it. Except in special cases such as the megger, both
the voltage and current quantities employed by the meter are
quite small.
This presents a problem for measurement of
low resistances, as a low resistance specimen may be of much
smaller resistance value than the meter circuitry itself.
Imagine trying to measure the diameter of a cotton thread
with a yardstick, or measuring the weight of a coin with a
scale built for weighing freight trucks, and you will
appreciate the problem at hand.
One of the many sources of error in
measuring small resistances with an ordinary ohmmeter is the
resistance of the ohmmeter's own test leads. Being part of
the measurement circuit, the test leads may contain more
resistance than the resistance of the test specimen,
incurring significant measurement error by their presence:
One solution is called the Kelvin, or
4-wire, resistance measurement method. It involves
the use of an ammeter and voltmeter, determining specimen
resistance by Ohm's Law calculation. A current is passed
through the unknown resistance and measured. The voltage
dropped across the resistance is measured by the voltmeter,
and resistance calculated using Ohm's Law (R=E/I). Very
small resistances may be measured easily by using large
current, providing a more easily measured voltage drop from
which to infer resistance than if a small current were used.
Because only the voltage dropped by the
unknown resistance is factored into the calculation -- not
the voltage dropped across the ammeter's test leads or any
other connecting wires carrying the main current -- errors
otherwise caused by these stray resistances are completely
eliminated.
First, select a suitably low resistance
specimen to use in this experiment. I suggest the
electromagnet coil specified in the last chapter, or a spool
of wire where both ends may be accessed. Connect a 6-volt
battery to this specimen, with an ammeter connected in
series. WARNING: the ammeter used should be capable
of measuring at least 5 amps of current, so that it will not
be damaged by the (possibly) high current generated in this
near-short circuit condition. If you have a second meter,
use it to measure voltage across the specimen's connection
points, as shown in the illustration, and record both
meters' indications.
If you have only one meter, use it to
measure current first, recording its indication as quickly
as possible, then immediately opening (breaking) the
circuit. Switch the meter to its voltage mode, connect it
across the specimen's connection points, and re-connect the
battery, quickly noting the voltage indication. You don't
want to leave the battery connected to the specimen for any
longer than necessary for obtaining meter measurements, as
it will begin to rapidly discharge due to the high circuit
current, thus compromising measurement accuracy when the
meter is re-configured and the circuit closed once more for
the next measurement. When two meters are used, this is not
as significant an issue, because the current and voltage
indications may be recorded simultaneously.
Take the voltage measurement and divide it
by the current measurement. The quotient will be equal to
the specimen's resistance in ohms. |
