Uncertainty calculation

Just let you know how to do uncertainty calculation. The entire machine in the earth is not 100% accurate. We need to reduce as less uncertainty as possible by two methods; arithmetic sum method or statistical approach method.

Linear Potentiometer

Introduction:                                                                                                              
The word linear can be referring to a straight line graph with voltage versus displacement. Consequently, the linear potentiometer is also called displacement transducers. The operation of this linear potentiometer is a voltage division on a hybride conductive film. However, there are a lot of types of linear potentiometer with different of products, design, specific range and displacement force. Here is the link http://www.waycon.biz/linearpotentiometers.html. This report is illustrated, measurement of output voltage after applying different displacement. The different displacements being apply the different voltage that can get.

Objective:

·         Performed adjusting the linear potentiometer displacement.
·         Performed measuring output voltage of linear potentiometer.
·         Recorded down the reading shown on multimeter of output voltage.

Criteria:
·         Correct process and work procedures while working on the linear potentiometer.
·         Make sure voltage supply equipment setting is correct set at 6V.
·         Make sure the reading is start from 0cm displacement of the linear potentiometer.

Tools and facilities or resources:
·         Linear potentiometer
·         Voltage supply equipment
·         Multimeter (at this experiment is using voltmeter)

Procedures:

1.      Prepared linear potentiometer, voltage supply equipment and multimeter (voltmeter) from George Jolley (lab assistant) or Dr. Geoffrey (academic lecturer) in engineering lab.

2.      Connected electrical wiring between linear potentiometer to the voltage supply equipment and the multimeter.

3.      Switched ON, the voltage supply equipment and the multimeter.

4.      Set the voltage supply equipment to 6V and turned the rotary switch of the multimeter to voltage and pointed the correct range of volt (V).

5.      Moved the pointer of linear potentiometer started at 0cm. The multimeter reading should be read at approximately 6V ± 0.2V. At here the reading has shown 5.8V.

6.      Move the pointer of linear potentiometer from 0 to 1cm and see the reading of the multimeter to measure the output voltage.

7.      Drop down and recorded every 1cm reading till 8cm of each voltage is shown.

8.      Repeated same experiment for twice to get more accurate reading by calculate average reading.

9.      After finish recorded, remember to switch off every equipment in engineering lab.

10.  Returned all the equipment to George Jolley.

 

Results:

Experiment to measure the output of a linear potentiometer

However there is no equipment is hundred percent accurate neither machinery nor human being.

Uncertainty:

·         Voltmeter Operating Uncertainty ± 2.00 percent.

Ø  The electronic circuits in the multimeter (voltmeter) produce to an uncertainty of ± 2.00 percent.

 

·         Voltmeter Resolution Uncertainty ± 0.005 Volts (0.08% at 6 volt point)

Ø  The voltmeter displays only two decimal places. This gives rise to a further uncertainty of ± 0.005 volts. At the result, this represents 0.08 percent of the displayed value if the instrument reads 6 volts.

Ø  The calculation is 0.005 x 100/6.0 = 0.083 ≈ 0.08%

Ø  0.005V due to < 0.005 ≈ 0.000 and > 0.005 ≈ 1.000

Ø  100 is 100 percent and it gives the percentage reading.

Ø  6.0 is 6V point of the setting in the voltage supply equipment.

 

·         Ruler Manufacturing Uncertainty ± 0.1mm (0.25% at 4cm point)

Ø  The ruler manufacturing process gives rise to an uncertainty of ± 0.1mm. As the result, at the 4cm (40mm) point this represents ± 0.25 percent.

Ø  The calculation is 0.1 x 100/40 = 0.25%

 

·         Ruler Resolution Uncertainty ± 0.25mm (0.63% at 4cm point)

Ø  Even if the ruler was totally accurate, the person using it would not read the indicated value with complete accuracy. The resolution uncertainty would vary depending on the eyesight of the user. Assume that this adds a further 0.25mm to the reading.

Ø  The calculation is 0.25 x 100/40 = 0.625 ≈ 0.63%

Consequently, the total measurement uncertainty of the output voltage can be calculated by simply adding all of the individual components. This experiment gives 4 cm point.

In fact, the experiment result shown at here is quite different by almost 3% compare to real life. It is because of several factors contributed to the measurement uncertainty to raise or lower down the value of the final result.

The other way to obtain uncertainty is using a statistical approach.  It is the best to repeat each measurement several times to determine more accurate reading by calculating average.

Calibration certificates stating for voltmeter and the ruler of probability distribution:

·         Normal distribution (divided by 2)

·         Rectangular distribution (1.732051)

·         Resolution has a rectangular distribution.

·         Repeatability is the exception to this rule because it has already gone through a statistical procedure.

Uncertainty Budget for 4cm point

To determine the expanded uncertainty budget, multiply the combined uncertainty by 2. To use the jargon, this gives the expanded uncertainty to a 95 percent confidence level. To certain that the output voltage, quote will be correct within ± 2.23 percent. (Calculated with longer decimal point that why not gets 2.22%) This is less than the uncertainty obtained using the Arithmetic Sum method.

 Analysis of the results:

1.      The results shown that statistical approach method (2.23%) have less uncertainty than arithmetic sum method (2.96%) that also means statistical approach method is more accurate.

2.      One of the reason statistical approach method more accurate is because it has been taken the value several times to avoid less calibration and eyes sight.

3.      The result of uncertainty is acceptable which not exceed 3% in real life.

4.      Uncertainly can be produced by calculation of decimal point, eyesight, length of wire (high resistance), wire of twisted (high resistance), and internal resistance of instrument equipment.

5.      The graph plotted should be straight line as name of “linear”.

6.      The longer distance of linear potentiometer, the smaller of the value of voltage output.

7.      The values of experiment 1, experiment 2, experiment 3 should be almost approximate the same ± 0.1 with average value.

8.      The average value is more accurate being plotted compare to experiment 1 graph.

 Comment/ Conclusion:

1.      The graph successfully being plotted.

2.      The entire instrument should be check for proper function before used.

3.      Refer to instruction or proper procedure or guide if not sure of using lab instrument.

4.      Take more experiment value to get more accurate reading.