Electrical Resistance Strain Gage

Table of Contents

Theory of Wheatstone Bridge Circuits …..page 3

Objectives вЂ¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦...page 7

Materials вЂ¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦..…..page 8

ProcedureвЂ¦Ð²Ð‚¦Ð²Ð‚¦.вЂ¦Ð²Ð‚¦page 9

CalculationsвЂ¦Ð²Ð‚¦page 10

Graph of DataвЂ¦Ð²Ð‚¦page 12

Data TableвЂ¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦..page 13

Pictures and Illustrations

Bibliography вЂ¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦Ð²Ð‚¦.вЂ¦Ð²Ð‚¦..…..page 14

History and Theory of the Wheatstone Bridge

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.

Here, Rx is the unknown resistance to be measured; R1, R2 and R3 are resistors of known resistance and the resistance of R2 is adjustable. If the ratio of the two resistances in the known leg (R2 / R1) is equal to the ratio of the two in the unknown leg (Rx / R3),

then the voltage between the two midpoints will be zero and no current will flow between the midpoints. R2 is varied until this condition is reached. The current direction indicates if R2 is too high or too low.

Detecting zero current can be done to extremely high accuracy . Therefore, if R1, R2 and R3 are known to high precision, then Rx can be measured to high precision. Very small changes in Rx disrupt the balance and are readily detected.

If the bridge is balanced, which means that the current through the galvanometer Rg is equal to zero, the equivalent resistance of the circuit between the source voltage terminals is:

R1 + R2 in parallel with R3 + R4

Alternatively, if R1, R2, and R3 are known, but R2 is not adjustable, the voltage or current flow through the meter can be used to calculate the value of Rx, using Kirchhoff's circuit laws. This setup is frequently used in strain gauge and Resistance Temperature Detector measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.

First, we can use the first Kirchhoff rule to find the currents in junctions B and D:

Then, we use Kirchoff's second rule to find the voltage in the loops ABD and BCD:

The bridge is balanced and Ig = 0, so we can rewrite the second set of equations:

Then, we divide the equations and rearrange them, giving:

From the first rule, we know that I3 = Ix and I1 = I2. The desired value of Rx is now known to be given as:

If all four resistor values and the supply voltage (Vs) are known, the voltage across the bridge (V) can be found by working out the voltage from each potential divider and subtracting one from the other. The equation for this is:

This can be simplified to:

The Wheatstone bridge illustrates the concept of a difference measurement, which can be extremely accurate. Variations on the Wheatstone bridge can be used to measure capacitance, inductance, impedance and other quantities, such as the amount of combustible gases in a sample, with an explosimeter. The Kelvin bridge was one specially adapted for measuring very low resistances. This was invented in 1861 by William Thomson, Lord Kelvin.

The concept was extended to alternating current measurements by James Clerk Maxwell in 1865, and further improved by Alan Blumlein in about 1926.

Objective

To measure the amount of strain in a cantilever beam using an electrical device called a strain gage. When we have recorded the results using the gage, then the values will be calculated using accepted methods and formulas based in theory. Whereupon the results of each will be compared and conclusions drawn.

Procedure

1) Gather up the materials needed and turn on the strain gage.

2) Adjust the gage by turning the SET ZERO knob to obtain a zero reading in the strain gage meter window.

3) Tare the weight of the C hook and load hanger by installing them on the beam and reset the zero as was done before.

4) Test the meter by carefully putting some pressure on the beam and observe the meter. It should show that a load was placed on the beam. Do this in both directions.

5) Add each of the known weight to the hanger one at a time.

6) Record the reading on the strain meter. Enter the data in the data table

7) Repeat step 6 for all the remaining weights.

8) Plot a graph of Load vs Strain using excel.

9) Then using the theoretical formulas provided