These results were taken using a power supply of e.m.f. 2.00V and the variable resistor at 1MΩ
These results were taken using a power supply of e.m.f. 2.00V and the variable resistor at 2MΩ
For all values of the variable resistor my results fit the general expected pattern, the potential difference across the thermistor will increase as the temperature decreases. For each of the experiments I have drawn a scatter graph for the potential difference against the temperature and then drawn in a line of best fit. I have used excel to work out the equation for each of these lines:
Experiment 1: y = -432.98Ln(x) + 295.36
Experiment 2: y = -23.035Ln(x) + 103.45
Experiment 3: y = -22.534Ln(x) + 86.192
Ln represents the natural log of x. To work out the equation for the three curves the natural log of x has to be plotted against y. The negative constant is the gradient of the line of the natural log of x against y and the other is the y-axis intercept.
The line of best fit for the graph of experiment 1 was the opposite shape to that of experiment 2 and 3. All three have a negative gradient and show strong negative correlation. However, for experiment 1 the gradient gets more negative as the temperature increases as opposed to the gradients for the curves in experiments 2 and 3, which get less negative as the temperature increases. This may be due to human error, which have caused odd results. It is unlikely to be systematic error as the only difference between the experiments is the value of the variable resistor; everything else is kept the same.
The value of the variable resistor is crucial in determining the sensitivity of this circuit in sensing temperature. This is because it is a potential divider and the potential difference has been divided up between the two resistors in the ratio of their resistances. The variable resistor in experiment 1 was at a much smaller resistance than the other two experiments. It was set at 1K as opposed to 1M and 2M. This means that the resistance of the thermistor between 0˚C and 40˚C would be much greater than the variable resistor so it would have a much greater potential difference across it. As it was, nearly all of the potential difference was across the thermistor. This would mean a small change in the temperature would only change the resistance slightly, which would only cause a small change in the potential difference across the thermistor. As nearly all of the e.m.f. was across the thermistor a small change in the potential difference would not be detected using a multimeter. This means that a lower value resistor than the thermistor that it is connected with as a potential divider would result in the sensor not being able to resolve small changes in the potential difference, which would mean it would be less sensitive. The experiments when the value of the variable resistor was much greater than the thermistor produced more accurate results and if used in sensing the temperature of something this potential divider would be able to resolve to a greater degree of accuracy than the one with a smaller value resistor in. The value that the variable resistor would take in a temperature-sensing device would depend on how sensitive the instrument was required to be. If the device needed to be extremely accurate and sense very small changes in temperature it would need a high value resistance compared to the thermistor. However, if its accuracy was less important then a lower value resistor would be suitable as small temperature changes would not be significant. The exact value of the resistor would depend on to what degree of accuracy and sensitivity the temperature sensor needs to work to.
By dividing the change in the input of the thermistor, the temperature, by the change in the output, the potential difference across the thermistor I can work out the sensitivity of my sensor. The more sensitive an instrument is, the greater the change of its reading for a given change of the variable causing the change.
Experiment 1: 40/170 = 0.235mV ˚C
Experiment 2: 40/74.13 = 0.540mV ˚C
Experiment 3 = 40/40.5 = 0.988mV ˚C
These results back up my earlier statement that the greater the value of the variable resistor the more sensitive the sensor is.
For experiments 2 and 3 the graph was more curved than for experiment 1. I already established why this was above. For experiments 2 and 3 the differences in potential difference increase as the temperature decreases. However, the opposite is true for experiment 1. I am not sure why this is. It may be down to the smaller value of the variable resistor or it could be down to human error or just coincidence.
The lines of best fit for the graphs of experiments 2 and 3 are both similar shaped curves whereas the line of best fit for the graph of experiment 1 looks like a reflection. I feel that this is due to human error and multimeter used not being sensitive enough. I would like to experiment further with the value of the variable resistor in experiment 1 with a more sensitive device to measure voltage. By taken more results with a more sensitive device I could be able to determine if the 1st experiment produced odd results.
The response time for my sensor was quicker than the mercury thermometer. However, the greater the value of the variable resistor the greater value the sensor can resolve to. So the more accurate sensor will take longer to respond.
For this circuit to produce an output that displays the temperature in ˚C or Kelvin the potential difference recorded across the thermistor would have to be processed and shown on a display (could be analogue or digital). To do this the potential difference across the thermistor would have to be sensed by another sensor and then this information would be processed using the appropriate equation given above. This data would then be shown on a display unit given an actual value for the temperature in its units.