# resistance measurement

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Related to resistance measurement: Current measurement, Voltage measurement

## Resistance measurement

The quantitative determination of that property of an electrically conductive material, component, or circuit called electrical resistance. The ohm, which is the International System (SI) unit of resistance, is defined through the application of Ohm's law as the electric resistance between two points of a conductor when a constant potential difference of 1 volt applied to these points produces in the conductor a current of 1 ampere. Ohm's law can thus be taken to define resistance R as the ratio of dc voltage V to current I, Eq. (1).

(1)
For bulk metallic conductors, for example, bars, sheets, wires, and foils, this ratio is constant. For most other substances, such as semiconductors, ceramics, and composite materials, it may vary with voltage, and many electronic devices depend on this fact. The resistance of any conductor is given by the integral of expression (2), where l is the length,
(2)
A the cross-sectional area, and &rgr; the resistivity. See Electrical resistance, Electrical resistivity, Ohm's law, Semiconductor

Since January 1, 1990, all resistance measurements worldwide have been referred to the quantized Hall resistance standard, which is used to maintain the ohm in all national standards laboratories. Conventional wire-wound working standards are measured in terms of the quantized Hall resistance and then used to disseminate the ohm through the normal calibration chain. These working standards can be measured in terms of the quantized Hall resistance with a one-standard-deviation uncertainty of about 1 part in 108. See Hall effect

The value of an unknown resistance is determined by comparison with a standard resistor. The Wheatstone bridge is perhaps the most basic and widely used resistance- or impedance-comparing device. Its principal advantage is that its operation and balance are independent of variations in the supply. The greatest sensitivity is obtained when all resistances are similar in value, and the comparison of standard resistors can then be made with a repeatability of about 3 parts in 108, the limit arising from thermal noise in the resistors. In use, the direction of supply is reversed periodically to eliminate effects of thermal or contact emf's.

The bridge is normally arranged for two-terminal measurements, and so is not suitable for the most accurate measurement at values below about 100 &OHgr;, although still very convenient for lower resistances if the loss of accuracy does not matter. However, a Wheatstone bridge has also been developed for the measurement of four-terminal resistors. This involves the use of auxiliary balances, and resistors of the same value can be compared with uncertainties of a few parts in 108.

Typically a bridge will have two decade-ratio arms, for example, of 1, 10, 100, 1000, and 10,000 &OHgr;, and a variable switched decade arm of 1–100,000 &OHgr;, although many variations are encountered. For the measurement of resistors of values close to the decade values, a considerable increase in accuracy can be obtained by substitution measurement, in which the bridge is used only as an indicating instrument. The resistors being compared can be brought to the same value by connecting a much higher variable resistance across the larger of them, and the accuracy of this high-resistance shunt can be much less than that of the resistance being compared. See Wheatstone bridge

The Kelvin double bridge is a double bridge for four-terminal measurements, and so can be used for very low resistances. The addition to its use for accurate laboratory measurement of resistances below 100 &OHgr;, it is very valuable for finding the resistance of conducting rods or bars, or for the calibration in the field of air-cooled resistors used for measurement of large currents. See Kelvin bridge

Measurements of resistances from 10 megohms to 1 terohm (1012 &OHgr;) or even higher with a Wheatstone bridge present additional problems. The resistance to be measured will usually be voltage-dependent, and so the measurement voltage must be specified. The resistors in the ratio arms must be sufficiently high in value that they are not overloaded. If a guard electrode is fitted, it is necessary to eliminate any current flowing to the guard from the measurement circuit. The power dissipated in the 1-M&OHgr; resistor is then 10 mW, and the bridge ratio is 106. The guard is connected to a subsidiary divider of the same ratio, so that any current flowing to it does not pass through the detector. Automated measurements can be made by replacing the ratio arms of the Wheatstone bridge by programmable voltage sources. An alternative method that can also be automated is to measure the RC time constant of the unknown resistor R combined with a capacitor of known value C.

An obvious and direct way of measuring resistance is by the simultaneous measurement of voltage and current, and this is usual in very many indicating ohmmeters and multirange meters. In most digital instruments, which are usually also digital voltage meters, the resistor is supplied from a constant-current circuit and the voltage across it is measured by the digital voltage meter. This is a convenient arrangement for a four-terminal measurement, so that long leads can be used from the instrument to the resistor without introducing errors. The simplest systems, used in passive pointer instruments, measure directly the current through the meter which is adjusted to give full-scale deflection by an additional resistor in series with the battery. This gives a nonlinear scale of limited accuracy, but sufficient for many practical applications. See Current measurement, Voltage measurement

## resistance measurement

[ri′zis·təns ‚mezh·ər·mənt]
(electricity)
The quantitative determination of that property of an electrically conductive material, component, or circuit called electrical resistance.

## Resistance measurement

The quantitative determination of that property of an electrically conductive material, component, or circuit called electrical resistance. The ohm, which is the International System (SI) unit of resistance, is defined through the application of Ohm's law as the electric resistance between two points of a conductor when a constant potential difference of 1 volt applied to these points produces in the conductor a current of 1 ampere. Ohm's law can thus be taken to define resistance R as the ratio of dc voltage V to current I, Eq. (1).

(1)
For bulk metallic conductors, for example, bars, sheets, wires, and foils, this ratio is constant. For most other substances, such as semiconductors, ceramics, and composite materials, it may vary with voltage, and many electronic devices depend on this fact. The resistance of any conductor is given by the integral of expression (2), where l is the length,
(2)
A the cross-sectional area, and &rgr; the resistivity. See Ohm's law, Semiconductor

Since January 1, 1990, all resistance measurements worldwide have been referred to the quantized Hall resistance standard, which is used to maintain the ohm in all national standards laboratories. Conventional wire-wound working standards are measured in terms of the quantized Hall resistance and then used to disseminate the ohm through the normal calibration chain. These working standards can be measured in terms of the quantized Hall resistance with a one-standard-deviation uncertainty of about 1 part in 108.

The value of an unknown resistance is determined by comparison with a standard resistor. The Wheatstone bridge is perhaps the most basic and widely used resistance- or impedance-comparing device. Its principal advantage is that its operation and balance are independent of variations in the supply. The greatest sensitivity is obtained when all resistances are similar in value, and the comparison of standard resistors can then be made with a repeatability of about 3 parts in 108, the limit arising from thermal noise in the resistors. In use, the direction of supply is reversed periodically to eliminate effects of thermal or contact emf's.

The bridge is normally arranged for two-terminal measurements, and so is not suitable for the most accurate measurement at values below about 100 &OHgr;, although still very convenient for lower resistances if the loss of accuracy does not matter. However, a Wheatstone bridge has also been developed for the measurement of four-terminal resistors. This involves the use of auxiliary balances, and resistors of the same value can be compared with uncertainties of a few parts in 108.

Typically a bridge will have two decade-ratio arms, for example, of 1, 10, 100, 1000, and 10,000 &OHgr;, and a variable switched decade arm of 1–100,000 &OHgr;, although many variations are encountered. For the measurement of resistors of values close to the decade values, a considerable increase in accuracy can be obtained by substitution measurement, in which the bridge is used only as an indicating instrument. The resistors being compared can be brought to the same value by connecting a much higher variable resistance across the larger of them, and the accuracy of this high-resistance shunt can be much less than that of the resistance being compared.

The Kelvin double bridge is a double bridge for four-terminal measurements, and so can be used for very low resistances. The addition to its use for accurate laboratory measurement of resistances below 100 &OHgr;, it is very valuable for finding the resistance of conducting rods or bars, or for the calibration in the field of air-cooled resistors used for measurement of large currents.

Measurements of resistances from 10 megohms to 1 terohm (1012 &OHgr;) or even higher with a Wheatstone bridge present additional problems. The resistance to be measured will usually be voltage-dependent, and so the measurement voltage must be specified. The resistors in the ratio arms must be sufficiently high in value that they are not overloaded. If a guard electrode is fitted, it is necessary to eliminate any current flowing to the guard from the measurement circuit. The power dissipated in the 1-M&OHgr; resistor is then 10 mW, and the bridge ratio is 106. The guard is connected to a subsidiary divider of the same ratio, so that any current flowing to it does not pass through the detector. Automated measurements can be made by replacing the ratio arms of the Wheatstone bridge by programmable voltage sources. An alternative method that can also be automated is to measure the RC time constant of the unknown resistor R combined with a capacitor of known value C.

An obvious and direct way of measuring resistance is by the simultaneous measurement of voltage and current, and this is usual in very many indicating ohmmeters and multirange meters. In most digital instruments, which are usually also digital voltage meters, the resistor is supplied from a constant-current circuit and the voltage across it is measured by the digital voltage meter. This is a convenient arrangement for a four-terminal measurement, so that long leads can be used from the instrument to the resistor without introducing errors. The simplest systems, used in passive pointer instruments, measure directly the current through the meter which is adjusted to give full-scale deflection by an additional resistor in series with the battery. This gives a nonlinear scale of limited accuracy, but sufficient for many practical applications. See Current measurement, Voltage measurement

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