PHYS 203 General Physics
Laboratory Session #5
Wheatstone Bridge
by
A. A. Tovar, Ph. D.
Introduction
A Wheatstone bridge is a measuring instrument invented by Samuel Hunter
Christie in 1833 and improved and popularized by Sir Charles Wheatstone
in 1843. It is used to measure an unknown electrical resistance by balancing
two legs of a bridge circuit, one leg of which includes the unknown component. Its operation is similar to the original potentiometer except that in
potentiometer circuits the meter used is a sensitive galvanometer.
Measuring Resistance
In the Wheatstone bridge circuit above, Rx is the unknown resistance to be
measured; R1 , R2 and R3 are resistors of known resistance and the resistance
of R2 is adjustable. The easy to derive “Balanced Bridge Condition” is
R1
R3
=
R2
Rx
(1)
This condition holds when there is no current going through the bridge (middle part of the circuit). When this happens the voltmeter will read zero volts
indicating a short circuit. So, if we vary R2 until this condition the voltmeter
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attached between points D and B read zero, then we can use the Balanced
Bridge Condition to determine the unknown resistance, Rx .
However, what if we use a potentiometer (pot.) as our adjustable resistor?
It has no readings, we will not know R2 . In this case, we can
1. Put a known resistor for R2 ,
2. Adjust the pot. to balance the bridge,
3. Replace R2 with a know resistance value, and measure the voltage
4. Repeat the last step several times, and build a “calibration curve.”
5. Put in a know resistor (WITHOUT balancing the bridge), read the
voltage off, and use the calibration curve to determine the resistance.
We will be doing this process in this lab.
Example Applications
• Measure unknown resistance values.
• Measure Light Levels (use Photoresistor)
• Measure Strain (use Strain Gauge)
• Measure Temperature (use Thermistor)
For example, we could use a Strain gauge under a door mat to determine
whether a person has entered or exited a room. We could then use that
as part of a circuit that starts a recording when the door mat is stepped
on that says “Yes, that’s Pete’s Bar and Grill!” (Of course, there are a lot
more practical applications. However, there is a LOT you can do with the
Wheatstone bridge which is why Charles Wheatstone ended up rich.)
Another Example Use of the Wheatstone Bridge
Problem:
Design a system to accurately determine the number of bolts put in a bucket.
This was done as part of a class project for a course as Penn State. (For more
info, google ”Wheatstone Bridge” weighing bolts).
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Solution:
Use a strain gauge on a cantilevered beam that holds a bucket. A Wheatstone
circuit is used to convert an electrical resistance change of the strain gauge
to a weight measurement.
Here’s a graph of their setup:
Here’s their calibration curve:
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Activity 1: Potentiometer
A potentiometer (pot) has 3 terminals. The resistance between to 2 furthest
terminals is constant. The resistance between either one of these terminals
and the middle terminal varies as the screw is turned.
1. Put a 10K Pot. in a circuit board.
2. Using the DMM as an Ohmmeter, record each of the resistance values.
Turn the screw and repeat the process, filling out the following table
as you go:
Data Point
1
2
3
4
5
6
7
R12 (Ω)
R23 (Ω)
R13 (Ω)
Activity 2: Wheatstone Bridge
Connect the following circuit:
• Use the power supply set to 5 V.
• For simplicity, choose R1 , R3 , and Rx to have the same approximate
values. Use resistance values around 5 kΩ.
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• Use a 10 kΩ Pot.
• With the DMM measuring DC Volts, adjust the pot. so that the bridge
is balanced (there is zero volts reading on the DMM).
• Take 5 resistors between 1 kΩ and 8 kΩ, and get a voltage reading,
filling out the following table:
Data Point Resistance (kΩ) Voltage (mV)
1
2
3
4
5
• Plot your data on a graph. Is it a straight line? If so, determine the
slope (in mV/kΩ).
• Take two ”unknown” resistors, measure the voltage read by your Wheatstone Circuit, and use your graph to determine the resistance of these
resistors. Check your answers against a conventional Ohmmeter.
Conceptual Questions
Wilson, Ch. 20, do Conceptual Questions 13-19.
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