4.3. Measuring Bridges

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Linette Stafford
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1 ask 1. Wheatstone bridge is shown in figure 1 and is being used to deterine changes of the resistance X. X Figure 1. Measuring bridge for deterining changes in resistance Derive the expression for the voltage of the easuring diagonal as a function of ΔX, if the bridge is balanced when ΔX = 0 Ω, and the instruent and the power supply can be considered ideal. In case the supply voltage is = 5 V, peranent resistance = 100 Ω, and the resistance X = Ω, what will be the easured voltage across the bridge? Will anything change in the above calculus if the voltage source is replaced by a current source of adequate power: I = 50? Kako je ost u ravnoteži za ΔX = 0 Ω, sledi da je X (1.1) Kada je ost priključen na naponski izvor, napon na ernoj dijagonali iznosi: V V X X 1 X (1.) Za date podatke, izračunava se da je napon na ernoj dijagonali 5 V 0,1Ω 1,9 V (1.3) 100 Ω 0,1Ω ko se ost priključi na strujni izvor jačine I napon erne dijagonale će biti.3-1

2 V V I 0,1Ω Ω 1,97 V 100 Ω 0,1Ω I I X (1.) Dakle, napon dijagonale osta se proenio za 1,9 V 1,97 V 0,3μV (1.5) ask. he easuring bridge shown in figure is used to verify terination resistance of a long subscriber line. Peranent resistors in bridge legs are 100 Ω. What will be the easured voltage across the bridge in cases the line is terinated using the following resistances: 100 Ω, Ω, 10 Ω, as well in cases it is short-circuited and open-circuited. ssue the resistance of the line itself is negligibly low. =? Figure. Measuring bridge for deterining terination resistance. apon na dijagonali osta je V V 1 (.1) Kada je Δ = 0 Ω, napon na dijagonali je Kada je Δ = 0,1 Ω <<, napon na dijagonali je približno 0 (.) (.3) 000 Kada je Δ = 0 Ω ~, napon na dijagonali je.3-

3 (.) Za otvorenu vezu se dobija da izraz (.1) postaje V V li li 1 (.5) Za kratku vezu, izraz (.1) se svodi na V V (.6) Ovo je veoa efikasan način da se voltetro sa široki radni opsego odredi ispravnost teriniranja ISD agistrale. ko je napon veoa ali (reda /000) ože se satrati da je linija ispravno terinirana, ko je napon nešto veći, i negativan linija je terinirana otpornošću većo od one koju propisuje standard, a ako je veći i pozitivan anjo otpornošću. Za slučajeve da je napon u dijagonali osta istog reda veličine kao i napon dijagonale, reč je o neteriniranoj ili kratkospojenoj agistrali, što se ustanovljava provero predznaka napona. ask 3. In the sae casing there are two separate Pt-100 thero-resistors. he task is to easure teperature of a reote water container in the range of 0 o C to 100 o C. he supply voltage for the bridge is = 5 V. he reote container where resistors are placed is 50 away fro the bridge circuit, so copper wires are being used to coplete the circuit. he paraeters of the copper wires are: S = 0.5 ρcu = Ω / αcu = αpt = 10-3 K -1 Coplete the bridge with peranent resistors so that the bridge is balanced at 0 o C. Deterine the easureent error after the water in container is heated up to 100 o C, and the abient teperature where copper cables lay changes fro 0 o C to 50 o C assuing the thero-resistors are attached to the bridge using two-wire-connection? What will change if three-wire-connection is used? his task is irrelevant for ESMS+ students since it exceeds the covered topics. esistivity of the copper at 0 o C is l Cu0 Cu 1.75 Ω (3.1) S t 0 o C resistances of copper wire and platinu resistor are.3-3

4 1 0 C 108 Ω 100 Ω (3.) Pt 0 Pt 1 0 C 1.89 Ω 1.75 Ω (3.3) Cu0 Cu t 50 o C the resistance of the copper wire will increase to While at 100 o C teroresistor will have 1 50 C.10 Ω 1.75 Ω (3.) Cu C 10 Ω 100 Ω Pt (3.5) Case of a two-wire connection When two-wire connection is used, the bridge looks like in Fig. 3. Cu Pt Cu Cu Pt Cu Figure 3. wo-wire connection equired resistors to balance the bridge at 0 o C are Pt Ω (3.6) 0 Cu0 When teperature of the water in the container rises to 100 o C the bridge should easure 100 Cu0 Cu0 Cu0 Cu V Cu0 (3.7) However, because the abient teperature changes, the resistance of copper wires also rises resulting in an incorrect reading of:.3-

5 V (3.8) So the easureent error in this case would be V V V 1.15 % (3.9) Case of a three-wire connection If a third wire is introduced to connect sensors to the bridge a ore robust bridge can be obtained. he principle schee of a three-wire connected bridge is shown in Fig.. Cu Pt Cu Cu Cu Cu Cu Pt Figure. hree-wire connection to the bridge his three-wire connection can also be applied when only one theral sensor is used. Copper cables connected to the instruent across the bridge will have no influence to the easureent results since the internal resistance of a volteter is exceeding the by several orders of agnitude. o balance the bridge peranent resistors should have values of 108 Ω (3.10) Pt 0 fter the teperature of the water rises to 100 o C, the instruent should read: 100 Cu0 Cu0 Cu V Cu0 Cu0 (3.11).3-5

6 ut in reality, because the copper wires will also heat up to 50 o C, a different value will be read: V (3.1) esulting in a significantly saller easureent error of V V V 0.17 % (3.13) ask. Cable bridge shown in Fig. 5 is used to deterine resistance difference between wires a and b in a twisted pair. oth peranent resistors in bridge legs have an equal value 1 kω. Potentioeter with a total of Max = steps has a total value of 100 Ω. 0 steps are being used when the slider is in the left-ost position and the easured value of the resistor in that case is 0 Ω. Figure 5. Cable bridge configuration he instruent balances the bridge when the slider is set at the M = 31 step. Deterine the resistance unbalance of wires a and b? Condition for the bridge to be balanced is y siplifying the above expression we obtain (.1) M (.) M ax.3-6

CHAPTER 2 ELECTROMECHANICAL INSTRUMENTS

CHAPTER 2 ELECTROMECHANICAL INSTRUMENTS CHAPTE 2 ELECTOMECHANCAL NSTUMENTS Learning Outcoes At the end of the chapter, students should be able to: Understand construction and operation of peranent agnet oving-coil (PMMC) instruent. Describe