Sensors & Measurement (ENT 164)
Laboratory Module
EXPERIMENT 2
THE WHEATSTONE BRIDGE
1. OBJECTIVE:
To analyze a basic Wheatstone bridge by determining the percentage error in an
unbalanced condition using Thevenin’s theorem.
2. COMPONENTS & EQUIPMENTS:
1 dc power supply
1 galvanometer
1 digital multimeter
3 resistors, 2.2kΩ ± 5%
1 resistor, 2.7kΩ ± 5%
1 potentiometer 10kΩ
3. 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 2.1: Open-circuit Wheatstone bridge
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Laboratory Module
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 V and V
which represents Thevenin’s equivalent voltage:
a
b
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.
4. PROCEDURE:
1. Measure the actual value of the resistors R1, R2, R3 and R4 and record them in
Table 2.1.
2. Construct the circuit as shown in the Figure 2.2 below:
Figure 2.2: Basic Wheatstone bridge
3. Apply 10 V to the circuit and record the galvanometer current as Ig3 in Table 2.1.
4. Disconnect the galvanometer from the circuit of Figure 2.2 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 2.3. Connect the galvanometer to the output terminals a and b.
Measure the galvanometer current and record it in the table as Ig1.
Sensors & Measurement (ENT 164)
Laboratory Module
Figure 2.3: 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 2.2:
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 2.1.
7. Next, determine the deflection current in the galvanometer, Ig2, by using the
following formula:
I g2 =
Vth 2
; where Rg = internal resistance of galvanometer = 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 2.2.
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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Laboratory Module
Name:____________________________ Matrix No.:_____________ Date:_________
5. RESULT
Table 2.1
Resistor
Values, R (kΩ)
Galvanometer
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 2.2
Percentage of Error, e % =
calculated − measured
× 100%
calculated
Ig2 and Ig3
Ig1 and Ig2
Vth1 and Vth2
Rth1 and Rth2
Instructor Approval: ………………………………….
Date: ……………………
Sensors & Measurement (ENT 164)
Laboratory Module
Name:____________________________ Matrix No.:_____________ Date:_________
5.3 Calculation
Instructor Approval: ………………………………………….
Date: ………………
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Laboratory Module
Name:____________________________ Matrix No.:_____________ Date:_________
5.3 Calculation
Instructor Approval: ………………………………………….
Date: ………………
Sensors & Measurement (ENT 164)
Laboratory Module
Name:____________________________ Matrix No.:_____________ Date:_________
6. DISCUSSION
7. CONCLUSION
Instructor Approval: ………………………………………….
Date: ………………
Sensors & Measurement (ENT 164)
Laboratory Module
Name:____________________________ Matrix No.:_____________ Date:_________
PROBLEMS
1. What does bridge null or balanced mean? What happens in a bridge circuit to
make it balanced?
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2. Name the bridge which is a modified version of the Wheatstone bridge and the
purpose of its modification.
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