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Introduction & Theory
With the exception of superconductors, all conductors have electrical resistance. The resistance of a conductor varies with composition, geometry, temperature, pressure, fields, and other factors. In this experiment, the variation of resistance with temperature will be investigated.
For most common conductors, the dependance of resistance on temperature is minimal under mild conditions; however the resistance of some materials varies strongly with changes in temperature. These materials are useful in thermistors, electronic devices used to determine temperature.
The flow of electricity through a circuit is similar to water in a pipe in many respects. The addition of pressure at one point in the pipe can cause flow and ejection of water at some distant point in the point. Similarly, electrons are pushed through a circuit by applied potentials. The difficulty in moving an electron from one molecule to another gives rise the resistance. In materials such as metals with a sea of electrons, resistance is very low. In insulators such as glass and rubber, it is difficult to transfer electrons between atoms and resistance is high. Other materials, known as semiconductors, can have high or low resistances depending on the conditions. In the case of the thermistor, the increase in molecular motion due to temperature increases allows electrons to be transferred between molecules easier. As a result, the resistance is relatively high at low temperatures and lower at high temperatures.
The use of a thermistor as a temperature reading device has several advantages. The use of small amounts of semiconductor material, and the small heat capacity that accompanies it, results in short response times to temperature changes. In addition, the use of electrical current in measurement lends itself directly to technological applications. Using a computer and other available electronic instruments, plots of conditions versus temperature and temperature versus time can be quickly, accurately, and repeatedly created and stored for future analysis.
One problem with computerized analysis using thermistors involves the nature of the signal obtained. The source signal exists as a resistance, which a computer has no inherent means of determining. The most straightforward measurement of resistance involves applying a potential across the resistor and measuring the effects. Fortunately, the voltages and currents computers are designed to work with are not sufficient to heat the resistor merely by measuring it.
Materials and Methods
A glass encapsulated thermistor in the end of a long (~ 2 foot) sealed glass tube was placed in a deep thermostatted water bath, at the same level as a thermometer with the leads running to a circuit as shown in the attached laboratory notebook page. Using a variable thermostat, the temperature of the water bath was varied and the voltage drop across the resistor measured at several temperatures. The voltage drop was used to determine the resistance of the thermistor and compare it to the expected resistance for the temperature given by the manufacturer.
Table 1 - Comparision of Results to Expected Values Temperature
% Difference 10.5
Summary of Results
Linear regression can be applied to the data given by the computer for A/D value and voltage to obtain a perfectly fitting (correlation=1) relationship between the two.
Sources of error in this experiment include loose connections, temperature variations as measurements were taken, and resolution limitations of the apparatus.
The prototyping board used in the experiment coupled with the stranded leads coming from the thermistor lead to occasional readings of 0 from the A/D convertor. When this occurred, the run was repeated to obtain data without discordant values.
The time required to actually take a measurement was fairly lengthy, and it is likely that the temperature of the water bath changed slightly as the measurement was taken. While efforts were make to assure the bath temperature was stable before taking measurements, time limitations limited margins of safety. The size of the water bath was also fairly large (several liters) and as a result was slow to change temperatures. A smaller bath would have required less time to equilibrate, but been more susceptible to random errors.
The A/D converter reported to the CPU in integer values, so the maximum resolution was 1 unit. Values of 560 to 1510 are limited to 0.18% and 0.062% precision respectively. These tolerances are fairly small, and need only be noted to determine significant digits. For future experiments, it would be feasible to update the BASIC program used to determine the number of significant digits and only report to that precision.
1. Specification sheet for Yellow Springs Instrument Company glass encapsulated thermistor, provided in handout.