The results for the negative coefficient were taken to the nearest 5 ohms because accuracy was not important.
Sensor Terms
Sensor: Sensors are systems that measure or respond to changes in their surroundings. In this case the thermistor responds to changes in temperature by increasing/decreasing resistance.
A sensor is a device designed to produce an electrical signal in response to a change in its surroundings, either caused by a change in a specific physical variable or by the movement of surrounding objects.
Sensitivity: The ratio of output for a given input.
The sensitivity of a measuring instrument is the change of its output divided by the change in input.
A temperature sensor whose output changes by 100 mV for a change of 2 K in its input has a sensitivity of 50 mV per Kelvin.
In an instrument in which the change of the reading is directly proportional to the change of the variable causing the reading, a graph of the reading (on the y-axis) against the variable (on the x-axis) would be a straight line through the origin. The gradient of the line is equal to the sensitivity, which is the same across the full range of the instrument because the line is straight.
In a system or an instrument in which the change of reading is not proportional to the change of the variable causing the reading, the graph would be a curve. In this case, the sensitivity would vary with input. Many instruments, such as light meters, have a logarithmic dependence of output on light input.
Resolution: Resolution concerns the ability to detect small changes or differences.
The resolution of an instrument is the smallest change of the input that can be detected at the output.
For a digital instrument, the output is a numerical display. The resolution is the smallest change of input the instrument can display. For example, a digital voltmeter that gives a read-out up to 1.999 V has a resolution of 0.001 V if the smallest change in potential difference it can display is 0.001 V.
For an analogue instrument, the output is the position of a pointer on a scale. Its resolution is the smallest change in input that can be detected as a movement of the pointer. The resolution of an analogue instrument can be improved using a magnifying lens to observe movement of the pointer.
Set up: My experiment will be set up using a Wheatstone bridge circuit. It enables resistance to be measured much more accurately than by an ammeter. It involves making adjustments until a galvanometer is undeflected and so it does not depend on the accuracy of an instrument. Other known resistors are required however. The diagram below shows the set up of the Wheatstone bridge circuit:
4 resistances P, Q, R, S are joined together as in the diagram above.
P = Q = 47Ω
R = Variable resistor
S = Thermistor
M = Multimeter
When 3 Volts is placed across the circuit, P and Q are equal which means that R and S must be equal for the multimeter to read zero. (2 Potential Dividers in parallel)
P/Q = R/S
Method: I firstly set up the circuit as shown above and also set up a flame-proof mat, a Bunsen burner, a tripod and gauze, a beaker and a thermometer. The thermometer was held in place by a clamp and boss so my readings were much more reliable. However the temperature was still observed by my eye and so still unreliable.
Next, I took my beaker and filled it with water about a quarter of the way up and placed ice and (if necessary) salt, to lower the temperature to 0ºC. Once this temperature was reached, I placed the thermistor into the water and switched the multimeter on. I then changed the resistance of the variable resistor until the multimeter showed a value of zero. Once done, I took the reading off the variable resistor to produce my results. This was then repeated for temperatures every 10ºC up to 100ºC. The entire experiment was then repeated another 4 times so that I could acquire an accurate average.
Having obtained my results, I then produced a graph of Average Resistance against Temperature. Having completed this, I then worked out my errors by taking the difference between the repeated resistance furthest away from the average resistance and the average resistance. This produced my error bars.
This completed, I then worked out my sensitivity by dividing each average resistance by the temperature (Output / Input). From this I then produced a graph of sensitivity against temperature. This is the same as working out the gradient of the tangent at various points on the graph.
Errors: There are two types of error:
Systematic error – Same direction and roughly same size.
Random error – Varying in size and direction.
There is a very small possibility that any random errors will occur on more than one occasion due to the experiment being carried out 5 times thus producing an average. Systematic errors will almost always occur in any experiment because there is almost no chance of having a 100% accurate reading. This means that I will have to look at my results and decipher which of my results, if any, are systematic errors.
There are various means of getting errors in my experiment:
The exact temperature may not be reached every time I take a reading because it was very hard to keep the temperature constant when I was taking readings from the higher temperatures. This means that for one repeat, I could have taken my readings when the temperature was 83ºC and the next repeat could have been taken when the temperature was at 78ºC.
Poor connections in my circuit could have increased resistance so any of my results could have been anomalies.
Resolution: From my plotted graph of Average Resistance against Temperature, I obtained my resolution results by drawing lines from my error bars across to the line of best fit and then down to the x-axis. I then measured the distance between the vertical lines. My results are shown below:
Conclusion: From my results I can state that as temperature increases, average resistance decreases. I can also state that I have no anomalies in my average resistance because the line of best-fit travels through every error bar on my graph.
When the temperature is low, the average resistance is very high and has large error bars. The results were very far apart and so producing an element of inaccuracy to my experiment.
From my results for resolution, I can conclude that my results show that as temperature increases, so does resolution.
I think that overall the experiment was conducted and executed well with no apparent disastrous inconveniences. There was however, a very small problem, which I encountered during the course of the experiment. The original thermistor that I began to use for my preliminary experiment decided to cease to function. This resulted in a loss of time, as I had to repeat my preliminary experiment so that any results conducted were not fair.
