From all the choices above, the potentiometer is chosen because it is more related to the work in the syllabus and it is one of the most accurate ways to measure among the others that have been suggested. To make the sensor more sensitive, another variable resistor is used to allow it to become more sensitive. The physics will be explained afterwards as a potential divider.
- Set up the circuit with two variable resisters, three 1.5V batteries, a multimeter (set up to measure the voltage, in volts).
- The circuit will be set up with other variable resister will have the lowest resistance to make the sensor more sensitive so that it can be accurate and experiment will all be done on the same day to get sensible results.
- The potentiometer is put vertically so that paper can put underneath however because there is a gap between the slide about 100 sheets of paper thick therefore to set it starting with zero, 2 rulers are put underneath which has equal thickness as 100 sheets of paper.
- Then results can be recorded. The experiment is done 3 at least 3 times, and then produces a calibration curve.
- A variable resistor which will affect the sensitivity of the whole experiment
- Number of pieces of paper varies from 1 – 200 pieces and is measured when each set of 10 pieces are put on to the sensor to a give sensible set of results
- The number of batteries only stay at 6V because that gives a steady range for the voltmeter to have readings from 0V => 6V
- Voltmeter acts like a device which presents the changes that has been made by the different amount of paper
- make sure all the wires are connected correctly and are properly insulated before use, to reduce the chance of being electrocuted
- make sure all the apparatus works properly (e.g. multi-meter is working properly with enough batteries)
- prevent getting paper cut from the paper
- papers are stacked properly so all the papers are measured by the potentiometer to get more accurate results
Preliminary results and Prediction
The following table show the preliminary results that is tested to show the about trend of the experiment.
- 1.5 V Battery x 4
- log scale potentiometer x 1
- voltmeter x 1
- variable resistor x 1
- some wires
- papers x 200 pieces
Diagram of the Circuit
How does a potential divide work?
A potential divider circuit is one that contains more than one resistor in series. The output to the circuit is taken across a certain number of these resistors and therefore the voltage can be controlled. The amount of voltage is dependent on the ratio of the resistors
This can also be set up with a variable resistor instead of separate resistors. The length of the resistor that has the voltage measured across it will determine the amount of voltage output.
The sensitivity of a sensor can be determined by the ratio of the two resistors. If the fixed resistor is very large in comparison to the detector then small changes will go unnoticed therefore in the experiment another variable resistor is used and is put to the smallest resistance.
The maximum voltage of the sets of results is 5.75V and minimum voltage is 0.17 V although the maximum potential difference across the position sensor is not 6V, the total voltage of the battery is 6V. It is because there is internal resistance inside the battery. By V=IR, if a thing have resistance, there will be a potential difference across the thing. e.g. If there is a 6V battery connected to two resistors with 0.1ohm and 100ohm, the potential difference across the 0.1ohm resistor = 6 X( 0.1/(0.1+100)) =0.005994V which is not equal to zero. Other than that there is a variable resistor and resistance in wires although they are very small.
Table of results
The following table shows the results I have recorded. There are 3 sets of experimental results and one set of result that is the average of the three reading that I have recorded so it the inaccuracy can be lower down and anomalous results can be seen clearly.
From the results, it shows the general trend is when the number of sheets of paper increases the voltage increase.
There are two anomalies results and in the graphs the anomalies are ignored. In conclusion from my results, the general trend of the results is when the voltage increase as the number of paper in the sensor increases. That is because as the number of paper increases the thickness of the paper increase which is measured by the slider at the potentiometer. The potentiometer works depends on the length and ratio between one ends to another in this case. In this case, as the thickness increase the length of one side of the potentiometer increase which cause the resistance of that side increase. With Ohm’s law, V=IR which means when R increase V increases therefore in my results it shows when number of paper increase, the voltage increases but not linearly because the potentiometer that has been used is a log potentiometer.
Calibration Curve – Average Results
The red lines on the graph show my attempts and trials. As you can see, my sensor can show pretty accurately the number of papers there is.
Reliability and Accuracy
The sensor is quite reliable because it produces quite an accurate calibration. From my testing, it can be seen that the results that I have produce is only ±1 paper error. It is pretty accurate considering with limiting accuracy of the potentiometer. However one more thing show be take into account is that the thicknesses of papers are different the paper that was being used to measure in the experiment was 0.0092 mm
There are two graphs above. The top one is the original graph plot from the results and the other one is to show the sensibility of the results taken.
The sensitivity = (150000 - 70000)/(72 -40)
=log 2500 sheets of paper/V
= 7.82 sheets of paper/V
It was a log graph after “un- log” it, it becomes a linear graph, so the gradient of the line will not change, so the sensitivity will not change, which remain 7.82 sheets of paper/V.
From the experiment and results that is given we can detect the numbers of sheets of paper from 1 sheet to 100 sheets. The small change which can be detected is 1 sheet from the graph we can see. That means that the resolution of the sensor is 1 sheet.
The error of the experiment
- The reading may not be accurate enough because the voltage that was shown in the multimeters has great fluctuation
- There is some resistance in the wires and internal resistance in the battery which will affect the result of the experiment.
- Since the temperature at any time will be slightly different from one another, so the reading may not be accurate enough.
- After long time of experiment the potentiometer starts to heat up. When the temperature increase, the resistance of the potentiometer will increase and the potential difference (voltage) will increase too, so the voltage that you read from this balance will be slightly larger than the real one. That means that the number of sheets of paper will also be slightly larger than the real one.
Improvement of the experiment
It is better to have a wider range of results, to do the experiment with the whole of the potentiometer because in the experiment only small part has been used. Other than that, what should be dependent on is not the number of paper should be both the thickness of the paper and the number of paper. Then a power supply should be used instead of batteries so it has a higher voltage which helps to increase the accuracy of the sensor. Another thing is a linear potentiometer should be used so readings can be read more easily although a log potentiometer does not give such large values.
Fitness for the purpose
Because the range of the position sensor is from 0N to 6.86N which is too small that we cannot use the position sensor to measure something which give out a lot of sheets of paper (length). So, it is a good choice to use the potentiometer to act like a sensor which measures some thinner sheets. However, we need to overcome the fluctuation of the voltage in multimeters so that we can have a wider range and more accurate results. However generally it can roughly tell the number of sheets of paper so it fits the purpose.
- Advancing Physics AS book, Institute of Physics Publishing, Britol and Philadelphia.
- Advancing Physics AS 2000 Student version (standalone), Institute of Physics Publishing, Britol and Philadelphia.