7.2 Resistance measurement
Devices that convert the measured
quantity into a change in resistance include the resistance thermometer, the
thermistor, the wire-coil pressure gauge and the strain gauge. The standard
devices and methods available for measuring change in resistance, which is
measured in units of ohms (Ω), include the d.c. bridge circuit, the
voltmeter–ammeter method, the resistance-substitution method, the digital
voltmeter and the ohmmeter. Apart from the ohmmeter, these instruments are
normally only used to measure medium values of resistance in the range of 1 Ω
to 1 MΩ. Special instruments are available for obtaining high-accuracy
resistance measurements outside this range (see Baldwin (1973)).
7.2.1 D.c. bridge circuit
D.c. bridge circuits, as discussed
earlier, provide the most commonly used method of measuring medium value
resistance values. The best measurement accuracy is provided by the null-output-type
Wheatstone bridge, and inaccuracy figures of less than ±0.02% are achievable
with commercially available instruments. Deflection-type bridge circuits are
simpler to use in practice than the null-output type, but their measurement
accuracy is inferior and the non-linear output relationship is an additional
difficulty. Bridge circuits are particularly useful in converting resistance
changes into voltage signals that can be input directly into automatic control
systems.
7.2.2 Voltmeter–ammeter method
The voltmeter–ammeter method consists
of applying a measured d.c. voltage across the unknown resistance and measuring
the current flowing. Two alternatives exist for connecting the two meters, as
shown in Figure 7.10. In Figure 7.10(a), the ammeter measures the current
flowing in both the voltmeter and the resistance. The error due to this is
minimized when the measured resistance is small relative to the voltmeter
resistance. In the alternative form of connection, Figure 7.10(b), the
voltmeter measures the voltage drop across the unknown resistance and the
ammeter. Here, the measurement error is minimized when the unknown resistance
is large with respect to the ammeter resistance. Thus, method (a) is best for
measurement of small resistances and method (b) for large ones.
Having thus measured the voltage and
current, the value of the resistance is then calculated very simply by Ohm’s
law. This is a suitable method wherever the measurement inaccuracy of up to ±1%
that it gives is acceptable.
7.2.3 Resistance-substitution method
In the voltmeter–ammeter method
above, either the voltmeter is measuring the voltage across the ammeter as well
as across the resistance, or the ammeter is measuring the current flow through
the voltmeter as well as through the resistance. The measurement error caused
by this is avoided in the resistance-substitution technique. In this method,
the unknown resistance in a circuit is temporarily replaced by a variable
resistance. The variable resistance is adjusted until the measured circuit
voltage and current are the same as existed with the unknown resistance in
place. The variable resistance at this point is equal in value to the unknown
resistance.
7.2.4 Use of the digital voltmeter to
measure resistance
The digital voltmeter can also be
used for measuring resistance if an accurate current source is included within
it that passes current through the resistance. This can give a measurement
inaccuracy as small as ±0.1%.
7.2.5 The ohmmeter
The ohmmeter is a simple instrument in
which a battery applies a known voltage across a combination of the unknown
resistance and a known resistance in series, as shown in Figure 7.11.
Measurement of the voltage, Vm, across the known resistance, R,
allows the unknown resistance, Ru, to be calculated from:
Ru
= R(Vb - Vm)/Vm
where Vb is the battery
voltage.
Ohmmeters are used to measure
resistances over a wide range from a few milliohms up to 50 MΩ. The measurement
inaccuracy is ±2% or greater, and ohmmeters are therefore more suitable for use
as test equipment rather than in applications where high accuracy is required.
Most of the available versions contain a switchable set of standard
resistances, so that measurements of reasonable accuracy over a number of
ranges can be made.
Most digital and analogue multimeters
contain circuitry of the same form as in an ohmmeter, and hence can be
similarly used to obtain approximate measurements of resistance.
7.2.6 Codes for resistor values
When standard resistors are being
used as part of bridge circuits, and also in other applications, it is often
useful to know their approximate value. To satisfy this need, coded marks are
made on resistors during manufacture. The two main styles of marking are a
four-band colour system and an alphanumeric code.
In the four-band coding system, the
resistance value and the maximum possible tolerance about that value are
defined by a set of four coloured bands. These are displaced towards one end of
the resistor, as shown in Figure 7.12, with band one defined as the band that
is closest to the end of the resistor.
Alphanumeric coding indicates the
resistance value using two, three or four numbers plus one letter. The letter
acts both as a decimal point and also as a multiplier for the value specified
by the numbers in the code. The letters R, K, M, G, T define multipliers of × 1,
× 103, × 106, × 109, × 1012 respectively. For example: 6M8 means 6.8 × 106,
i.e. 6.8 MΩ. 50R04 means 59.04 Ω. A separate letter indicating the tolerance is
given after the value coding. The meaning of tolerance codes is as follows:
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