Physics
Kelvin Bridge
The Kelvin Bridge is a specialized electrical circuit used to measure unknown electrical resistances with high precision. It is designed to minimize errors caused by lead resistance and contact resistance, making it particularly useful for accurate resistance measurements in laboratory settings. The bridge balances the ratio of known resistances to the unknown resistance, allowing for precise determination of the unknown resistance value.
Written by Perlego with AI-assistance
Related key terms
1 of 5
8 Key excerpts on "Kelvin Bridge"
- Stephen A. Dyer(Author)
- 2004(Publication Date)
- Wiley-IEEE Press(Publisher)
6 (5–7). In this bridge, the arm resistors A and B are advantageously replaced by two dc calibrators V A and V B having a very good linearity, a low temperature coefficient, and low output impedance. This bridge can be balanced auto- matically. At balance, the value of R x is given by the following equation: R x = V A V B R S (36) This type of bridge can be used to calibrate resistors from 10 M up to 1 T or more in less time and with lower uncertainty than with the conventional guarded Wheatstone bridge. Combined 314 BRIDGE INSTRUMENTS Dig. therm. R X R S V A V B GPIB controller D Figure 6. An automated guarded Wheatstone bridge. measurement uncertainties of order of 1 part in 10 5 can be obtained at 1 G with this bridge. Kelvin Double Bridge William Thomson (later Lord Kelvin) first described this bridge in a paper published in 1862. This network became known as the Thomson bridge, the Thomson double bridge, the Kelvin Bridge, and the Kelvin double bridge. According to F. Wenner (2), Thomson seems to have been the first to attempt measure- ments of the highest precision attainable with the apparatus then available and to have an understanding of the factors lim- iting the precision of measurement. As shown in the schematic diagram of Fig. 7, the circuit contains a second set of ratio arms, labeled a and b. The guard circuit is not represented in Fig. 7. This Kelvin Bridge may be transformed into an equiva- lent Wheatstone bridge. The network formed by arms a and b and by link k can indeed be transformed in the Y network by using the theorem of Kennelly. The detector indication will be zero when the voltage at node 2 equals the voltage at node 5. U 2 = A A + B I S + X + (a + b)k a + b + k (37) D S X k A B a b E I 1 7 2 5 6 3 8 4 Figure 7.
eBook - PDFPragmatic Electrical Engineering
Systems & Instruments
- William Eccles(Author)
- 2022(Publication Date)
- Springer(Publisher)
The Wheatstone bridge was invented in 1833 by … no, not Sir Charles Wheatstone (1802– 1875) but by Samuel Christie. It implements a concept sometimes called differential measurement. This circuit balances out the zero-strain voltage and gives a reading of just the voltage associated with the strain itself. The bridge in Fig. 3.5 has two strain gauges and two resistors in it. The two strain gauges are in the upper arms; the two resistors are in the lower arms. Figure 3.5: Strain-gauge bridge—two arms 62 3. INSTRUMENTATION A clever part of this circuit is in the placement of the strain gauges on the beam being stressed. One gauge, on the upper left, is attached to the bottom of the beam; the other gauge, on the upper right, is attached to the top of the beam. If the beam is being deflected downward, the top gauge (upper right arm) sees tension and positive strain while the bottom gauge (upper left arm) sees compression and negative strain. This doubles the sensitivity of the measurement. The two resistors in the lower arms of the bridge are precision resistors whose resistance is identical to that of the strain gauges. If for example we use 120- gauges, the bottom resistors will be 120 also. Analysis of this bridge circuit is done using the voltage-divider relationship. But remember that a voltage divider is a valid method only when the divider doesn’t “leak,” meaning that there is no current being drawn from the divider itself. That’s the situation here because we are going to put a voltmeter between the middle terminals of the bridge. That meter will draw only a very tiny current from the terminals (microamperes) and will barely affect the voltage dividers. Moreover, we will find that when the bridge is exactly balanced, i.e., all four resistances are exactly equal, the voltage between the terminals will be zero.
eBook - PDFElectrical Principles & Practice NQF4 SB
TVET FIRST
- Jowaheer Consulting and Technologies(Author)
- 2014(Publication Date)
- Macmillan(Publisher)
Such devices change their internal resistance according to the specific level of strain (or pressure, temperature, liquid level and so on) and serve as the unknown resistor R x . The galvanometer is replaced by a circuit that can be calibrated to record the degree of imbalance in the bridge as the value of strain or other condition being applied to the sensor. Another practical example is to use a Wheatstone bridge for the measurement of temperature and the temperature coefficient of resistance. The resistance of a wire varies with temperature. A coil of copper wire is immersed into a water bath. A Wheatstone bridge is connected to measure its resistance at various temperatures. By plotting a graph showing the relationship between temperature and resistance, you can find the temperature coefficient. Calculating errors in measurement One of the most important characteristics of any measuring instrument is its accuracy, expressed in terms of error ( e ) as follows: Error ( e ) = true value of quantity – measured value of quantity The error ( e ) is also called the absolute error and does not indicate precisely the accuracy of the measuring instrument. Generally, the relative error ( e r ) is specified: e r = true value of quantity – measured value of quantity true value of quantity The percentage relative error is expressed as: % e r = true value of quantity – measured value of quantity × 100 true value of quantity 43 Module 2: Measuring instruments If a minus sign is obtained when performing the calculation, the measured value of the quantity was too high. Example 2.3 The expected value of the voltage to be measured is 230 V. However, the measurement gives a value of 228,5 V. Calculate: 1. the absolute error 2. the percentage relative error. Given: true value = 230 V; measured value = 228,5 V Solution 1. Absolute error ( e ) = true value of quantity – measured value of quantity = 230 – 228,5 = 1,5 V 2.
eBook - PDF- Charles A. Gross, Thaddeus A. Roppel(Authors)
- 2012(Publication Date)
- CRC Press(Publisher)
349 Sensors and Instrumentation 7.5.1 Bridge Circuits Bridge circuits are widely used as sensor interface circuits . The principle employed is to measure the offset that results from the deviation of a sensor element (e .g ., resistance) from its nominal value . Bridges can form part of a null-seeking circuit, in which feedback is used to force the sensor element back to its nominal value . In this case, the output is measured as the amount of feedback required to null the bridge . Such null-seeking circuits are employed, for example, in accelerometers, where the feedback is used to keep the mov-ing element near zero deflection which maximizes linearity while helping to prevent damage from overdriving the moving element . The resistor Wheatstone bridge circuit consists of four circuit branches, each containing one resistor, as well as an ac or dc voltage bias . Each leg contains one resistor . If just one branch contains a variable resistor, the bridge is called ¼-active (“quarter-active”) . If there are two branches with varying resistors, the bridge is called ½-active (“half-active”) . Bridges with all four branches containing varying resistors are called full-active . Figure 7 .8 shows a ¼-active resistive bridge powered by a dc bias source V DC . The output of the bridge is the difference between the voltages V A and V B indicated in Figure 7 .8 . The resistor labeled R X is the resistor whose value is desired to be measured . This is often a sensor element, for example a thermistor (a temperature-sensitive resistor), a photoresistor (resistance changes with light intensity), a piezoresis-tor (a force-sensitive resistor used in pressure sensors and accelerometers), or a strain gauge (in which resistance depends on the amount of stretching) . The other three resistors labeled R f are fixed resistors . The value of R f is chosen V DC V B V A + + – – V OUT R f R f R f R x = R f + Δ R FIGURE 7.8 Wheatstone bridge circuit used to interface a resistive sensor.
- R. M. Marston(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
Bridges and C -R boxes 73 ΙΟμΗ to ÎOOH. Both of these types of instrument are derived from the ancient (1843) Wheatstone bridge circuit, and it is well worth studying this in order to learn the finer points of bridge design. The 1843 pattern Wheatstone resistance-measuring bridge uses the basic Figure 4.1 circuit and consists of a pair of d.c.-energized potential dividers (R 2 /R and R y IR x ) with a sensitive meter wired between them. R 2 and Ri have a 1:1 division ratio, and are known as the 'ratio arms' of the bridge; R x is the 'unknown' resistor, and R y is a calibrated variable resistor. In use, R x is fixed in place and R y is then adjusted until a zero or 'null' reading is shown on the meter, at which point the two dividers are generating equal output voltages and the bridge is said to be 'balanced' or 'nulled'; under this condition the ratio R y IR x equals R 2 IR equals unity, and the R x value thus equals that of R y the bridge's balance is not influenced by variations in energizing voltage. A major feature of this original version of the Wheatstone bridge is its very high null sensitivity. Thus, if the bridge is energized from 10V d.c, 5V is developed across all resistors at balance, and the meter reads zero volts; a shift of a mere 0.1 per cent will then give a 5mV reading on the meter. In prac-tice, this circuit can, when using a fairly simple null-detecting d.c. amplifiers, be expected to have a 'null sensitivity' factor (i.e. per-centage out-of-balance detection value) of about 0.003 per cent. A major disadvantage of this 1843 pattern bridge is that R y needs a vast range of values if it is to balance all possible values Figure 4.1. Original (1843) version of the basic Wheatstone bridge. 74 Instrumentation and Test Gear Circuits Manual Τ Ratio L / / ^ j a r m s i ^ T I A J ~jr À-ç M e t e r Figure 4.2. Conventional version of the Wheatstone bridge. of R x .
eBook - PDF- D. F. A. Edwards(Author)
- 2014(Publication Date)
- Butterworth-Heinemann(Publisher)
MEASUREMENT OF D.C. RESISTANCE 53 circuit whose resistance is to be measured but which connect two points in this circuit to the measuring circuit. These two points are known as the potential terminals, and serve to fix definitely the length of the circuit under test. In the methods used for the precise measurement of low resistance, the unknown resistance is compared with a low resistance standard of the same order as the unknown, and with which it is connected in Potential terminals Current terminals ' Fig. 3.10. Standard low resistance series. Both resistances are fitted with four terminals - two current terminals for connection to the supply circuit and two potential terminals for connection to the measuring circuit (Fig. 3.10). 3.6.1. Kelvin Double Bridge This is a development of the Wheatstone bridge and has the same advantages of quick and simple operation. An examination of the circuit (Fig. 3.11) shows that a current is passed through the standard resistance Fig. 3.11. Kelvin double bridge 54 MEASUREMENT OF D.C. RESISTANCE S and the unknown resistance R in series and the potentials developed across these are balanced by means of the bridge network. This method can be regarded as a combination of bridge and potentio-meter methods, having the advantages of both in that the actual balance is obtained by the instantaneous bridge method (i.e. not requiring any connections to be changed, as in the case of the potentiometer), but since the potentials are balanced against one another the contact resistance at the points of connection are not included in the measure-ment, as they would be in the Wheatstone method. In Fig. 3.11, cc represents the current terminals, and dd the potential terminals, of resistances R and S. At balance i g is zero and the same current flows through P and ß, and this is also the case with p and q and R and S. Then ii = z 3 , i 2 = U, an d i s = ß÷ · By Kirchhoff s second law, for mesh (1), i s R -i x P + i 2 p = 0, or i s R = i x P-i 2 p.
eBook - PDF- James Cameron(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
For resistance measurement, one of the fixed arms, say R 1? is replaced by the unknown resistor, and the bridge is balanced by a known adjustable resistor at one of the other positions. The values of the three known arms are then used in the ratio calculation to obtain the unknown arm's value. This circuit 56 3. BASIC ELECTRONICS FOR MEASUREMENT is rarely used directly for resistance measurement but is used in a wide variety of transducer applications. To list only one, the circuit of Fig. 3.18 could be used as a thermistor thermometer by replacing one of the arms of the bridge with a thermistor. A thermistor is a resistor constructed of special materials that give it a high negative temperature coefficient, i.e., as the temperature rises, the resistance falls. The temperature of the thermistor could be measured either by balancing the bridge and comparing the computed resistance with the temperature-resistance curve supplied with the thermistor or by measuring the unbalanced current or voltage. The output of a single thermistor will give a non-linear curve with temperature, but two matched thermistors may be employed in a bridge circuit to produce a resistance that is highly linear over useful ranges of temperature (Fenwal Bulletin L-9A). 3.6. ELECTRICAL MEASUREMENTS: VOLTAGE, CURRENT, RESISTANCE 3.6.1. The General-Purpose Voltmeter The most common and generally useful electrical measurement device is the hand-held or portable voltmeter. This can be constructed with a moving-coil type of panel meter, but the newer types are increasingly making use of a digital display, with liquid crystal displays (LCDs) becoming more common (Fig. 3.19). Voltmeters are generally equipped with two measuring leads, or probes, one black for the ground or relatively more negative connection and the other red for the positive connection. Most instruments are equipped with range switches to allow measurement of voltages in several ranges, both AC and DC.
eBook - PDFInstrument Technology
Measurement of Pressure, Level, Flow and Temperature
- E. B. Jones(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
If R = R 2 , and R 3 = T when the bridge is balanced, then changes in the resistance of the leads will affect both arms AD and CD equally, and the bridge will remain balanced. Four-lead connection This method of connection was introduced by Callendar in 1886, and is shown in Figure 4.56(b). Two identical pairs of leads are connected in the arms AD and CD of the bridge. The pair in the arm AD are connected together at a point near the thermometer bulb; while the second pair, which is in the arm CD, is connected to the thermometer resistance bulb. Both pairs of leads are enclosed in the same outer cover so that the leads in AD compensate for any MEASUREMENT OF TEMPERATURE 3 3 9 changes in the resistance of the leads in CD due to ambient temperature variations. 4 . 6 . 4 . 2 THE BALANCED WHEATSTONE's BRIDGE When the highest accuracy and sensitivity is required the balanced form of the Wheatstone's bridge is used to measure the resistance of the resistance-thermometer bulb. This method is described as a null method, because when the bridge is balanced the voltage across BD is reduced to zero. The sensitive galvanometer was generally used as a detector of unbalance, but in most modern instruments automatically balancing bridges involving electronic methods of detection are used. No special precautions need be taken to keep the voltage applied to the bridge constant as this does not alter the values of the resistances at which the bridge will balance. The method is also independent of the calibration of the unbalance detector. Any detecting circuit is suitable if it is sufficiently sensitive to detect small voltages, has a stable zero, and is robust enough for industrial use. (a) (b) Figure 4.56 Resistance thermometer lead systems In this method, the resistance of one arm, or in some cases more than one arm, of the bridge is adjusted until the bridge is balanced. This adjustment is made by hand in the manually operated instruments, but in others it is done automatically.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
