Bridge

Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.

Related TopicsElectrics, electrical circuit

IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].

Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge

1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.

2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by

, (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].

3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.

Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *） RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.

3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W

4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W

1.0 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.




1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is

balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.

2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].


Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *） RX/W2010

511/51/101/20*) Here, please note the unit of dIG is Div.



1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.









4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.


IntroductionWe have learned before how to measure the resist Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.




1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is

connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.



Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *）

RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.



1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?

For example: if the indication o Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.





2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by

, (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].





1.03.0 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.












1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the une Wheatstone bridgeGoal

Learn the operation of the Wheatstone bridge.





2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)

where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].





1.03.05.0 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.












1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+30 Wheatstone bridge

GoalLearn the operation of the Wheatstone bridge.





2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)

where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].









1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship:

. (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.







1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a re Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.






3. Uncertainty of a Wheatstone bridge

In procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.







1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse

adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.






1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For exa Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.


IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these

meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].




3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move

for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.



4. The measurement of RX at different power supply voltages.

According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.








3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)

Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W


1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For exa Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.


IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an

ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].









According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.











1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitan Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.












According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W












1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=3000 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
























1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=3000 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
























1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.

References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142.

2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华，陆申龙基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社北京 2004 pp. 165-168.





























3.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.

References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华，陆申龙基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社北京 2004 pp. 165-168.
















0*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.




















0*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.



5.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.


ce is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.





mple: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.

References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in

different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华，陆申龙基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社北京 2004 pp. 165-168.



mple: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.

References

1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华，陆申龙基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社北京 2004 pp. 165-168.



sistance box?Wheatstone Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.

Related Topics

Electrics, electrical circuit





3. Uncertainty of a Wheatstone bridge

In procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.












3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process.

Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.








Introduction

We have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].




3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one

tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.







bridgeGoalLearn the operation of the Wheatstone bridge.















a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.



















0*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.

References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327.

3. 沈元华，陆申龙基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社北京 2004 pp. 165-168.

7.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.


rtainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.




f the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.


ance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].




3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be

identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.





1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resista Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.




1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge.

The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.








IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.

In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].




3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)

Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.



4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.

Voltage/V RS/W R'S /W

1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistanc Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.




1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1)

Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.



Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *） RX/W2010511/5

1/101/20*) Here, please note the unit of dIG is Div.









Procedure

1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *） RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.



1.03.0

5.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discus Wheatstone bridgeGoalLearn the operation of the Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.




1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1)

Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.



Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *） RX/W2010511/5

1/101/20*) Here, please note the unit of dIG is Div.





Wheatstone bridge.


IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such mea Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.




1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current

flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.



Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *） RX/W




1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?

For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.


surements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].












s how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.









Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e.

the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *） RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.



1.03.05.07.09.0 Questions

1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.





e box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.





Fig. 1 Wheatstone Charles (1802-1875).

Fig. 2 The circuit diagram of a Wheatsone bridge




Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)

Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *） RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.



1.03.05.07.0

9.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.



















nce box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.



References

1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华，陆申龙基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社北京 2004 pp. 165-168.

a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.









Procedure1. Set up the circuit as shown in Fig. 2.

2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *） RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.



1.03.05.0

7.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.





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