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

44

33

22

11

RiRi

RiRi

24

31 RRRR

The Wheatstone Bridge: Example Calculate R1 in a Wheatstone bridge when it is balanced and

when R2 = 300Ω, R3 = 200Ω, R4 = 100Ω .

Answer:

600300100200

24

31 RRRR

24

31 RRRR

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’

If all resistors are the same value but R1 increases by δR then output becomes

4

3

2

1

RR

RR

2

1243

3

21

1

RRRRv

RRR

RRRv

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

MeasuredR2 (1kΩ nominal)R3 (1kΩ nominal)R4 (1kΩ nominal)

By measured R2, R3, R4, calculate R1 for a balanced bridge.

24

31 RRRR

R1 for a balanced bridge

Calculated Measured

R1 (Ω) Caculated Vout Measured Vout

100200300400500600700800900

100011001200

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?