Experiment 23

The Wheatstone Bridge

Objectives

To learn the use of the Wheatstone bridge in measuring resistances and capacitances.

Introduction

The most convenient, and also the most accurate, method of measuring resistances of widely different values is by means of the Wheatstone bridge.  A Wheatstone bridge is a circuit consisting of four resistors arranged as shown in Fig. 1.  It is used for finding the value of an unknown resistance by comparing it with a known one.  Three known and adjustable resistances are connected with the unknown resistance, a galvanometer, a power supply, and a key, as shown in Fig. 1.  For a condition of balance no current flows through the galvanometer.  Hence the current through R₁ is the same as the current through R₂, and the current through R₃ is the same as that through R₄.  Also, the potential drop across R₁ is equal to that across R₃.

1)             i₁R₁ = i₂R₃

Similarly, the potential drop across R₂ is equal to that across R₄

2)             i₁R₂ = i₂R₄

Dividing the first equation by the second, one finds the relation

3)            R₁/R₂=R₃/R₄

Therefore, if three of the resistances are known, the fourth may be calculated by using the above relation.

In the slide wire form of the bridge, as shown in Fig. 2, the resistances R₁ and R₃ are replaced by the uniform wire AB with a sliding contact key at C.  Since the wire is uniform in cross section, the resistances of the two portions are proportional to the lengths, hence the ration R₁/R₂ is equal to the ration AC/CB.  If R₃ is represented by a variable known resistance R, and R₄ by the unknown resistance X, the relation becomes

4)            AC/BC=R/X

Procedure 1

1)             Connect the slide wire form of the bridge as shown in Fig. 2.  Let X be the unknown resistance of resistor No. 1 and let R be the standard resistance.  Have the circuit approved by the instructor.  Read the color code and record the values of your three resistors.

2)             Measure the resistance of No. 1 with this bridge.  To obtain a balance, set the sliding key in the center of the bridge wire and adjust the control key, C, until a minimum deflection of the galvanometer is observed.  The sliding contact should be moved only when the contact edge is not touching the wire.

3)             When the galvanometer shows NO deflection on tapping the contact key C, proceed with the final adjustments, but do not shift the sliding key more than a fraction of a millimeter each time, until again the galvanometer shows no deflection.  Record the setting of the standard resistance and of the sliding key.

4)             Similarly measure the resistance of resistors No. 2 and 3.

5)             Compare the values obtained from the Wheatstone bridge against the values from the color code on the unknown.

Procedure 2

1)                   Repeat Procedure 1 with a known capacitor in place of the known resistor, measuring two unknown capacitances.  You must use the green (AC) terminals of your power supply and replace the galvanometer with an oscilloscope.  You will see an sine wave on the scope and as you adjust the tap on the slide wire, the sine wave flattened to zero amplitude replaces the zero reading on the galvanometer as the null condition.  Watch out! The voltages ratios across the capacitors are inverse to what they are in resistors.  That is, V₁/V₂ = C₂/C₁  instead of R₁/R₂.

2)                   Now measure the two unknown capacitors in parallel and compare the result with the value calculated from the formula for capacitors in parallel.  Is the formula correct?

Finally, connect the two unknown capacitors in series and check the series formula as well.