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ENT 164/4
SENSORS & MEASUREMENT
ENT 164/4
SENSORS & MEASUREMENT
LABORATORY MODULE
EXPERIMENT 4
WHEATSTONE BRIDGE
NAME
MATRIC NO
DATE
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ENT 164/4
SENSORS & MEASUREMENT
EXPERIMENT 4: WHEATSTONE BRIDGE
1.
OBJECTIVE
1.1 To analyze a basic Wheatstone bridge by determining the percentage error in an
unbalanced condition using Thevenin’s theorem.
2.
EQUIPMENTS / COMPONENTS
•
•
•
•
•
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3.
1 digital multimeter
3 resistors, 2.2 kΩ
1 resistor, 2.7 kΩ
1 potentiometer 10 kΩ
1 DC power supply
Breadboard
INTRODUCTION
When the Wheatstone bridge is in an unbalanced condition, current flows through the
galvanometer (connected between a and b of Figure 2.1), causing a deflection of its
pointer. The amount of deflection is a function of the sensitivity of the galvanometer. A
more sensitive galvanometer will deflect its pointer by a greater amount for the same
current.
To determine the amount of deflection that would result for particular degree of
unbalance, the Thevenin’s theorem is applied. Since we are interested in determining the
current through the galvanometer, the Thevenin’s equivalent voltage, VTh, and
Thevenin’s equivalent resistance, RTh, are to be determined.
The Thevenin’s equivalent voltage is found by disconnecting the galvanometer from
the bridge circuit, Figure 2.1, and determining the open-circuit voltage between terminals
a and b.
Figure 4.1: Open-circuit Wheatstone bridge
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By applying the voltage divider equation, the voltage at point a and b can be
determined. Therefore, the voltage between a and b is the difference between Va and Vb
which represents Thevenin’s equivalent voltage:
Vth = Vb – Va = Va – Vb
Thevenin’s equivalent resistance can be determined by replacing the voltage source,
V with a short circuit and then find the resistance by looking into terminals a and b.
For this experiment, we are going to use a digital multimeter to replace the
galvanometer’s function. Discuss the different occurs with these changes.
4.
PROCEDURE
1. Measure the actual value of the resistors R1, R2, R3 and R4 and record them in
Table 4.1.
2. Construct the circuit as shown in the Figure 4.2 below:
Figure 4.2: Basic Wheatstone bridge
3. Apply 10 V to the circuit and record the multimeter current at galvanometer’s
location as Ig3 in Table 4.1.
4. Disconnect the multimeter from the circuit of Figure 4.2 and calculate its
Thevenin’s equivalent circuit by looking back into the terminal a and b and using
the measured values for the resistor R1, R2, R3 and R4. Show steps of calculation
at the respective spaces. Record Vth1 and Rth1 in the table.
5. Construct the Thevenin’s equivalent circuit as calculated in the previous step as
shown in Figure 4.3. Connect the multimeter (replace galvanometer’s location) to
the output terminals a and b. Measure the multimeter current and record it in the
table as Ig1.
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Figure 4.3: Thevenin’s equivalent circuit
6. Apply and calculate the following approximations of Thevenin’s equivalent
voltage and Thevenin’s equivalent resistance to the original circuit of Figure 4.2:
Δr
⎛
⎞
Vth 2 = V × ⎜
⎟ and
⎝ 4 R + 2 Δr ⎠
Rth 2 =
R R ( R + Δr )
+
2
2 R + Δr
where,
R = 2.2 kΩ
Δr = R4 – R
Show the steps of calculation and record the value in Table 4.1.
7. Next, determine the deflection current in the multimeter, Ig2, by using the
following formula:
Vth 2
I g2 =
; where Rg = internal resistance of multimeter = 1 Ω
Rth 2 + R g
8. Calculate and record the percentage of error between the Ig2 and Ig3, and between
Ig1 and Ig2 in Table 4.2.
9. Calculate and record the percentage of error between Vth1 and Vth2.
10. Calculate and record the percentage of error between Rth1 and Rth2.
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5.
RESULTS
Table 4.1
Resistor
Values, R (kΩ)
Multimeter
Current, Ig (A)
Thevenin’s
Equivalent Circuit
R1 =
Ig1 =
Vth1 =
Approximate
Thevenin’s
Equivalent Circuit
Vth2 =
R2 =
Ig2 =
Rth1 =
Rth2 =
R3 =
Ig3 =
Δr =
R4 =
Table 4.2
Percentage of Error, e % =
calculated − measured
× 100%
calculated
Ig2 and Ig3
Ig1 and Ig2
Vth1 and Vth2
Rth1 and Rth2
5.3 Calculations
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6.
DISCUSSIONS
7.
CONCLUSION
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