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FACULTY OF ENGINEERING
LAB SHEET
EPM1016 Instrumentation & Measurement Techniques
TRIMESTER 3 2012-2013
IM1: Wheatstone and Maxwell Bridges
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Wheatstone and Maxwell Bridges
Precautionary steps:

Read the lab sheet thoroughly and carefully before coming to your lab session.

Take precautions for safety. Also handle the equipments carefully to prevent any damages.

Try to get as much of the analysis done during the lab session.
Objectives:

Construct the basic Wheatstone bridge measure voltages in an unbalanced bridge for different
configurations and verify the unknown resistors.

Construct the Maxwell bridge to measure the values of unknown resistance and inductance of
an inductors.
Apparatus:
 DC power supply.
 Breadboard
 Digital Multimeter
 Function Generator.
 4 resistors of 2.2 k ± 5%.
 2 resistors of 3.3 k
 1 resistor each of 51, 1 k, 10 k and 4.7 k.
 3 potentiometers of, 5 k,10 k and 100 k
 1 inductor of 2.5mH.
 1 capacitor of 10nF
Part I. WHEATSTONE BRIDGE
1.1
Theory
The basic Wheatstone bridge has been used extensively since the earliest days of electricity. It is
still widely used in a large number of null-type instruments. A null reading is obtained on a
Wheatstone bridge by a comparison of the voltage drops in the passive resistance arms of the
bridge. When the equation R1R4 = R2R3, for the circuit of Figure 1.1 is satisfied, the bridge is
balanced and a “null” or zero reading is obtained on the detector.
Consider the Wheastone's bridge shown in Figure 1.1. It has four arms each having a resistance.
The voltage at the nodes A and B may be computed using the simple potential division rule as
below:
VA 
R3
.VS
R1  R3
(1.1)
VB 
R4
VS
R2  R4
(1.2)
2
The voltage across the nodes A and B measured in the voltmeter would equal the difference
between the voltages at nodes A and B:
VAB  VA -VB =
R3
R4
VS VS
R1  R3
R2  R4
(1.3)
When the Wheatstone's bridge is balanced, the voltage VAB would equal zero. Thus in that
condition, equating VAB to zero in equation (1.3), one gets:
V AB =
On re-arranging, one gets:
R3
R4
VS VS = 0
R1  R3
R2  R4
(1.4)
R3
R4
=
.
R1  R3 R2  R4
(1.5)
Thus one may derive:
R1R4 = R2R3
(1.6)
R2
R1
VS
VAB
A
R3
B
R4
Figure 1.1: Wheatstone's bridge
1.2 Error
Percent of error for every reading taken against the computed values using the formula given below:
% error 
Ameasured - Acalculated
 100%
Acalculated
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Part A:
Procedure:
1. Construct the Wheatstone's bridge according to the circuit diagram given in Figure 1.1, where
R1 = R2 = R3 = 2.2 k.
2. Switch on the DC power supply and adjust the variable voltage source to show VS = 12V.
3. Measure the voltage across the point A and B, then, determine the % error between the
measured and the computed values according to the resistor values given in Table 1.1.
Table 1.1
Resistance, R4 ()
VAB (volts)
Computed
Measured
% error
1k
2.2k
3.3k
Part B:
Procedure:
1. Construct the Wheatstone's bridge according to the circuit diagram given in Figure 1.1,
where R1 = 3.3 k, R2 = 2.2 k, R4 (variable resistor) = 5 k and Vs = 12V.
2. For every value of R3 given in Table 1.2, adjust the variable resistance R4 until the bridge is
balanced. (Hint: value of VAB reduces to zero or smallest possible value)
3. Measure the value of R4 and tabulate the readings in Table 1.2.
4. Compute the expected value, R4c for every value of R3 given in Table 1.2.
5. Determine the percentage error (%error) for every reading taken against the computed
values.
Resistance, R3
Table 1.2
Measured value of R4 when
% error
Computed value of R4c
VAB  0 volts
2.2k
3.3k
4.7k
(Hint: Verify the given resistor value)
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Part II. MAXWELL BRIDGE
2.1
Theory:
The AC Bridge, a natural outgrowth of the DC bridge, consists in its basic form of four bridge arms,
a source of excitation, and a null-detector. The source of excitation is an AC signal at the desired
frequency. The detector may be a set of an ac voltmeter, an oscilloscope, or another device capable
of responding to alternating currents.
i2
i1
Z2
Z1
Vac
A
D
Z3
B
Z4
Figure 2.1 General ac bridge
The general form of an ac bridge is given in Fig. 2.1. The four bridge arms Z1, Z2, Z3, and Z4 are
shown as unspecified impedances. The bridge is said to be balanced when the detector response is
zero. One or more of the bridge arms are varied to balance the bridge so that a null response is
obtained. The condition for bridge balance requires that the potential difference from A to B be zero.
This happens when the voltage at node A equals the voltage at node B, in both magnitude and phase.
In complex notation we can write
VZ1  VZ 2
; and
VZ 3  VZ 4
i1Z1  i2 Z 2
i1Z 3  i2 Z 4
(2.1)
Dividing the equation,
Z1 Z 2

Z3 Z 4
(2.2)
Z1Z 4  Z 2 Z 3
(2.3)
If the impedances are written in polar form, Z, where Z represents the magnitude and  the
phase angle of the complex impedance. Equation(2.3) can be rewritten as
(Z11 )( Z 4  4 )  (Z 2  2 )( Z 3  3 )
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(2.4)
To multiply these complex numbers we multiply the magnitudes and add the phase angles. Thus,
equation (2.4) can be rewritten as
Z1 Z 4 (1   4 )  Z 2 Z 3 ( 2   3 )
(2.5)
Equation (2.5) shows that two conditions must be met simultaneously when balancing an ac bridge.
The first condition is that the magnitude of the impedances satisfy the relationship
Z1Z 4  Z 2 Z 3
(2.6)
The second condition requires that the phase angles of the impedances satisfy the relationship
(2.7)
1   4   2   3
This expression states that the sums of the phase angles of the opposite arms must be equal
2.2 Maxwell Bridge
The Maxwell bridge shown in Fig. 2.2 measures an unknown inductance in terms of a known
capacitance. Observing the bridge, we can see that
 Z1 
and
R1
1  jwR1C1
;
Z 2  R2
Z 3  R3
;
Z 4  R x  jwLx
Substituting these expressions into Equation (2.6) and separating the real and imaginary terms
yields
Rx 
R2 R3
R1
(2.8)
Lx  C1 R2 R3
(2.9)
Both Equations (2.8) and (2.9) must be satisfied for the bridge to be balanced.
C1
Vin
R2
R1
A
B
G
R3
RX
LX
Figure 2.2 Maxwell Bridge.
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2.3 Q-factor of an Inductor
The quality of an inductor is defined in terms of its power dissipation. For an ideal inductor,
the winding resistance should have zero resistance, and hence zero power dissipated in the
winding. For a lossy inductor which has a relatively high winding resistance, dissipates some
power. The quality factor or Q-factor of the inductor is the ratio of the inductive reactance and
resistance at the operating frequency f.
Q
X s L X

Rs
RX
(2.10)
where LS and RS, refer to the components of an RL series equivalent circuit. Q-factors for
typical inductors range from a low of less than 5 to as high as 1000 (depending on frequency).
2.4 Procedure:
1. Construct the ac bridge according to the circuit diagram shown in Fig. 2.2 with the
following components:





C1 = 10 nF
R1 (variable resistor) = 100 k
R2 (variable resistor) = 10 k
R3 = 51 
Inductor, L = 2.5 mH
(Hint: Verify the given C1 and R3 values)
2. By using the function generator, generate a 10 kHz sinusoidal signal with Vpp = 12V supply
across the bridge circuit. (Hint: use the oscilloscope to determine the supply Vpp)
3. Balance the bridge by varying the resistors R1 (from 5k to 95k) and R2 (from 1k to
9k).
4. Remove R1 and R2 from the circuit and measure and record their values into table 2.1.
5. Compute the parameters given in Table 2.1 accordingly.
6. Measure the dc resistance of the inductor, Rx.
7. Compute the percentage of error between the measured and computed values of Rx.
Table 2.1
No.
1
Parameter
2
R2
3
LX
4
RX
5
Q
6
ZX
7
RX
Computed
R1
7
Measured
% Error
3. EXERCISE:
a) Explain the term 'sensitivity of the bridge'.
b) For each measurement in part I (B), determine whether VA > VB or VA < VB. Explain to
support your answers.
c) In part II experiment,
(i) By using the computed Lx and Rx, compute the total impedance of the inductor using the
X
expression Z X  R X2  X L2 and   tan 1  L
 RX

 .

(ii) If the resistor of R3 and capacitor C1 available in the laboratory is 100  and 0.5 nF
respectively. Evaluate your setup in part II to determine the component values of the
variable resistor R1 and R2 to balance the computed Lx and Rx values in the Maxwell
bridge.
4. GUIDELINE FOR LAB REPORT AND SUBMISSION:
a) The report should contain the following:
 Objective of the experiment.
 Basic theory and schematic diagrams.
 Tabulation of the observed and computed data.
 Answers to the exercise questions.
 Conclusions.
b) You are given ONE WEEK to prepare and submit your lab report to the lab staff.
c) All reports can be handwritten or typed. Neatness and carefulness will be taken into account
in the marking of your report.
d) You MUST use the FOE lab report cover template. The template can be downloaded at
http://foe.mmu.edu.my/v2/lab/form/student_lab-report_cover-1%202010.doc
e) Prepare your own lab report and use your own findings and results.
f) Please be instructed that plagiarism is an academic offence and if similar reports are found,
you should be required to give an explanation for the similarities and no marks will be given
for both the original and the copied ones.
g) Late submission of your lab report will not be usually entertained unless if there is any
emergency cases and strong proof for late submission. Otherwise, automatically awarded 0
(zero) mark for the late submission.
h) This lab report carries 5% of the total course marks.
MARKING SCHEME
Total: 50% scale to 5%
1. Report content (Objective, theory and conclusions) – 10%
2. Experiment Results (observed and computed data) – 30%
3. Exercise – 10%
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