Download Week-9

Principles of Computer Engineering:
Lecture 4: The Wheatstone Bridge
Overview



Introduction to the Wheatstone Bridge
Use of the bridge to determine unknown resistances
To show that the bridge behaves in a non-linear fashion
The Wheatstone Bridge



We use an “Ohmmeter” to measure an unknown resistance
The heart of the simplest Ohmmeter is a so-called “Wheatstone
Bridge” circuit
If R1 was a variable resistor, we can adjust it until Vab = 0
The Balanced Wheatstone Bridge

When Vab = 0, a special condition occurs: the bridge is said to be
“balanced”, i.e. Va = Vb

This implies that ig = 0, hence from KCL, i4 = i3 and i2 = i1
Further, from Ohm’s Law & KVL; i4R4 = i2R2 and i3R3 = i1R1

The Wheatstone Bridge continued

Hence
i1 R1
i3 R3

i2 R2 i4 R4
R3
R1 
R2
R4
The Wheatstone Bridge: Example

Calculate R1 in a Wheatstone bridge when it is balanced and
when R2 = 300Ω, R3 = 200Ω, R4 = 100Ω .
R3
R1 
R2
R4

Answer:
R3
200
R1 
R2 
300  600
R4
100
Principles of Computer Engineering:
Experiment 4: The Wheatstone Bridge
Wheatstone Bridge

When the bridge is balanced
there will be no voltage across the
terminals ‘a’ and ‘b’
R1 R3

R2 R4

If all resistors are the same value
but R1 increases by δR then
output becomes
 R1
R3   R  R 1 
  v
v

 
 R1  R2 R3  R4   2R  R 2 
Procedure





Setup bridge circuit on breadboard with three 1k
resistors in bridge with resistance box as R1
Use power supply to provide 10V to the bridge
Adjust R1 until balance is reached (i.e. Vab = 0)
Now vary R1 from 100Ω to 1200Ω to give 12 different
outputs up to balance point
Plot the graph of R1 vs. Voltage
Measured
R2 (1kΩ nominal)
R3 (1kΩ nominal)
R4 (1kΩ nominal)
R3
R1 
R2
R4
By measured R2, R3, R4, calculate R1 for a balanced bridge.
R1 for a balanced
bridge
Calculated
Measured
R1 (Ω) Calculated Vout
100
200
300
400
500
600
700
800
900
1000
1100
1200
Measured Vout
Graph of Voltage vs. Resistance
Summary





Set up a Wheatstone Bridge circuit and verify its behaviour
for different balance conditions
Show that the bridge behaves non-linearly
Consider sources of errors in this experiment
Put all your results and notes into your logbook!
Any questions?