Lab III Wheatstone Bridge

Lab III Wheatstone bridge

Goal

Learn the operation of the Wheatstone bridge.

Related Topics

Electrics, electrical circuit

Introduction

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

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

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Fig.1 Wheatstone Charles (1802-1875).

Fig.2 The circuit diagram of a Wheatsone bridge

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1. A Wheatstone bridge circuit

As shown in Fig. 2, the unknown resistor RX and the other three adjustableresistors RA, RBandRS form a circuit called a "bridge". A galvanometerG (a sensitive current meter)is connectedto two points,2 and 4. In operation, we adjust the resistance of RStill the current flowing through the galvanometerIGis zero. This process is called "balancing" of the bridge. The galvanometerG isconnected there exactly for balancing the bridge. When the bridge is balanced, the current passingthrough the resistors RA, andRB is the same, and that passing through RS and RX is the same. Wethen have the relationship:

. (1)

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

1. Sensitivity of a Wheatstone bridge

In 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, atiny change of the resistorRS, described asδRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG·RS /δRS. Obviously, the larger theM is, more accurately the RSfor 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,RGis the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].

1. Uncertainty of a Wheatstone bridge

In procedure, the resistorRSis adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuitdepends 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 δRSwill 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 device

Three ZX21A resistors, an unknown resistor (about 2kΩ), an85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.

Procedure

1. Set up the circuit as shown in Fig.2.
2. MeasureRX at different values of RA /RB. (Set the voltage of power supply to 3V.)

Set RAand RBaccording to RA /RBvalues given in Table1. Adjust RSuntil IG equals to zero.DetermineRXat different RA/RBvalues.R'S is the measured resistance when IG is 2μA, i.e. thesmallest division the galvanometer scale.Fill out the table and find for which value of RA /RB,the sensitivity of Wheatstone bridge is largest.

Table 1Data table when RB=2000

*) Here, please note the unit of IG is Div.

1. MeasureRX 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: RXshould 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 bridgeis largest.

Table 2Data table when RA=RB

1. The measurement of RX at different power supplyvoltages.

According toTable 2,set RA, RBand RA/RX when the sensitivity M isthe largest. Carry out the measurement at different power supplyvoltages and fill out theTable 3. How is M dependent on the power supplyvoltage?

=______,=______,=______。

Table 3Data table at different power supplyvoltage.

Questions

1. Derive the equation (1).
2. Determine the measurement uncertainty of RXwhen the sensitivity M is thelargest 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%+0.02

1. Discuss how is measurement uncertainty of RXon different values of RA/RB, RA/RXand the power supplyvoltages.

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.

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