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1150
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Jan 9, 2024
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EMT1150 Lab Manual (08/2020)
1
EMT1150 Lab Experiment
Wheatstone
Bridge Circuit
Objective:
Understand the principle of Wheatstone bridge circuit, determine
the load voltage of bridge circuit, and use bridge circuit to measure unknown
resistor.
8.1 Wheatstone bridge circuit
A bridge circuit is a special class of circuits that can be used for measuring resistance, capacitance,
and inductance.
A resistance bridge is especially useful when a very accurate measurement of a
resistance is required.
The Wheatstone bridge or four arm bridge, invented by C. Wheatstone in
1843, is the most widely used resistance bridge for measuring resistance values.
A Wheatstone bridge as shown in Figure 8.1,
is nothing more than two simple series-parallel
arrangements of resistances connected between a voltage supply terminal and ground
.
A typical
Wheatstone bridge circuit has two input terminals (A and B) and two output terminals (C and D),
consisting of four resistors configured in a diamond-like arrangement as shown. Usually a
galvanometer or Multimeter is connected between two output terminals and one resistor, such as
R3, is adjustable. When the output voltage is zero, this is called balanced bridge condition.
Let’s analyze the bridge circuit.
Based on Voltage divider rule,
ܸ
=
ܸ
ௌ
ܴ
ଶ
ܴ
ଵ
+
ܴ
ଶ
ܸ
=
ܸ
ௌ
ܴ
௫
ܴ
ଷ
+
ܴ
௫
Figure 8.1 Wheatstone bridge circuit
EMT1150 Lab Manual (08/2020)
2
When bridge is balanced
,
ܸ
=
ܸ
, so
ܸ
ௌ
ܴ
௫
ܴ
ଷ
+
ܴ
௫
=
ܸ
ௌ
ܴ
ଶ
ܴ
ଵ
+
ܴ
ଶ
ܴ
௫
ܴ
ଷ
+
ܴ
௫
=
ܴ
ଶ
ܴ
ଵ
+
ܴ
ଶ
ܴ
௫
(
ܴ
ଵ
+
ܴ
ଶ
) =
ܴ
ଶ
(
ܴ
ଷ
+
ܴ
௫
)
ܴ
௫
ܴ
ଵ
+
ܴ
௫
ܴ
ଶ
=
ܴ
ଶ
ܴ
ଷ
+
ܴ
ଶ
ܴ
௫
ܴ
௫
ܴ
ଵ
=
ܴ
ଶ
ܴ
ଷ
ோ
య
ோ
ೣ
=
ோ
భ
ோ
మ
(Resistance ratio at balance)
ܴ
௫
=
ோ
మ
ோ
య
ோ
భ
(Find unknown resistance)
This formula proves that an unknown resistor Rx can be calculated in Wheatstone bridge circuit,
if the value of R
1
, R
2
and R
3
are known.
Wheatstone bridge circuit has many applications in real world. Most of the industrial sensors like
temperature, strain, humidity, displacement, liquid level, etc. produce the change in value of the
resistance for a variable change. The sensors can be connected into a Wheatstone bridge circuit,
then the resistance change can be measured. After calibration, the corresponding temperature,
strain, humidity, displacement, liquid level, etc. can be estimated.
Exercise 8.1
Potentiometer
1.
Test the connection of potentiometer. There are three legs in potentiometer, measure the
resistance between different legs.
Turn the knob to three different positions.
Table 8.1
R
AB
R
BC
R
AC
Position1
Position2
Position3
C
R1
±²Nȍ
Key=A
40 %
A
B
Figure 8.2 Potentiomster
0.03
9.52
9.53
3
44
3
S
EMT1150 Lab Manual (08/2020)
3
Question:
Conclude the function of potentiometer.
Exercise 8.2
Build bridge circuit
1.
Construct the following circuit with the potentiometer at the
maximum value.
Only close
the switch when you are making measurements.
2.
Close the switch. Measure voltages around the Loop. Measure and record the voltages
around Loop 1(E, V
R1
, V
R1
) and Loop 2 (E, V
R2
, V
R3
). Pay attention to polarity of the
measurements. Record data into Table 8.2.
Table 8.2
Loop1
Loop2
E
E
V
R1
V
R3
V
R2
V
R4
Sum of V
R1
and
V
R2
Sum of V
R3
and
V
R4
Question:
Use the measurements of Loop1 and Loop2 to prove KVL.
Figure 8.3 Wheatstone bridge circuit
E
9V
R1
³´µNȍ
R2
¶´·Nȍ
R4
·´¸Nȍ
S1
D
E
F
G
C
B
A
M
±²Nȍ
Key=A
100 %
R3
To make
it
easy
to
change
resistance
9
23
9
23
4.19
5.02
0.020
9.23
5.23
3.78
0.020
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EMT1150 Lab Manual (08/2020)
4
3.
Close the switch. Measure voltages to a Common Reference Point (GROUND), G.
Measure the voltage between
the following points to Ground point.
Table 8.3
V
A
V
B
V
C
V
D
V
E
V
F
V
M
Question:
Compare these voltages with measurement in part2, and explain the similarities and
differences. Hint: use the concepts of double-subscript notation and single-subscript notation.
4.
Measure and record the current supplied by the battery (I
total
) and the current through
each branch. The branch #1 consists of R1 and R2, the branch #2 consists of R3 and R4.
Table 8.4
I
total
I
1
I
2
Question:
Compare the current supplied by the battery to the sum of the currents through each
branch.
9.230 9.230
9.230
3.780
OV
OV
5.020
These
voltages
are
relatively
the
same
the
source
is
the
same
VD
is
like
Upitry
and
Vm
is
like
VRzs.rs
1.4mA
0.4mA
1mA
They
are
equivalent
EMT1150 Lab Manual (08/2020)
5
5.
Resistance Measurements, record data in Table 8.5
a.
Open the switch in circuit. (Isolate the components being measured).
b.
Measure and record the resistance in Branch
# 1.
c.
Measure and record the resistance in Branch
# 2.
d.
Measure and record the Total resistance in the circuit.
Table 8.5
R
total
R
branch1
R
branch2
Question:
Show your calculations.
6.
Balance the bridge.
a.
Close the switch and measure the voltages between the Point D and Point M.
V
DM
=
b.
How could you obtain this voltage from the measurements made in steps 2 and 3?
c.
3ODFH D /RDG UHVLVWRU ±². ³ EHWZHHQ 3RLQW 0 DQG 3RLQW '´ 0HDVXUH WKH /RDG
voltage (V
Load
)
V
Load
=
d.
To balance the bridge, adjust the potentiometer (R3) so that there is no voltage
across the Load resistor. Remove potentiometer from the circuit and measure the
resistance, check whether it follows the ratio formula derived before.
R3
(Pot)
=
Check ratio:
6.361452
10.29141
16.69141
IR.tR.IN
R
tRulRt
6.36km
4.714
5.614
10.319
1014
16.814
1.230
159mV
5.55191
EMT1150 Lab Manual (08/2020)
6
ோ
య
ோ
ర
=
ோ
భ
ோ
మ
=
Exercise 8.3
Measure an unknown resistor
1.
Pick up any resistor from your lab kit which is
LQ WKH UDQJH EHWZHHQ ²N WR ²µN ´
Measure the resistance of this resistor, fill in Table 8.6.
Treat this resistor as an unknown
resistor, use Wheatstone bridge circuit to measure the resistance.
2.
Build a bridge circuit, use this unknown resistor to replace R4 in Figure 8.3.
3.
Adjust the potentiometer to balance the bridge again. Remove potentiometer from the
circuit and measure the resistance, calculate the resistance of unknown resistor.
Table 8.6
Nominal value of
R
Unknown
Measurement of
R
Unknown
Measurement of
R3
(pot)
Calculation of
R
Unknown
Question:
Show your calculations.
Questions:
1)
Calculate each voltage in exercise 8.2.2 and compare it to the measured value.
2)
Calculate each current in exercise 8.2.4 and compare it to the measured value
3)
Calculate the resistances in exercise 8.2.5 and the total resistance and compare it to
the corresponding measured values.
4)
Of what advantage is it to measure voltage to a common point (or ground)?
58
4
0.82
4
1
0.841
3.3192
3.24142
2.71km
3.741952
3
14km
3.314
5
73.314
165
3.314
165
3.47142
73.314
165
3.141952
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7
5)
Research Resistance thermometer on internet, discuss how to use bridge circuit
to measure the temperature change.
-----------
L
AB
E
XPERIMENTS
E
NDS
H
ERE
,
P
ROCEED
W
ITH
L
AB
R
EPORT
-----------------
1
4.714
5.614
10.314
R
1019
6.819
16.8K
By
V12
Vt
91
9
0.62
9
5.980
4
Rt
6.36192
V34
Vt
Y
z
V34
9
5.58
3.420
V4
2
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A thermopile is constructed with chromel-alumel materials. Five junctions are maintained at 400-C
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potentiometer. Answer the following questions:
a) Draw the equivalent circuit and indicate all the given information.
b) What is the voltage induced by the potentiometer?
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Table 8.30
Temperature.
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-150
-100
<-50
<<-25
0
25
50
75
100
150
200
300
400
500
600
800
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1500
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QUESTION 2 '
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Besides temperature measurement that is based on thermal expansion, there are also
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R2
G
RTD
RRTD
Ri
E,
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