Resistance vs Temperature

Resistance vs. Temperature Elements of Physics Lab 231, section 231006 Lab Instructor: Usama al-Binni Experiment Performed on: September 28, 2009 Date Report is Submitted: October 5, 2009 Purpose and Method: The Resistance Versus Temperature experiment utilized a temperature controlled water reservoir in conjunction with the wheatstone bridge apparatus and a digital volt-ohm meter to measure the resistance as a function of temperature for a thermistor and a coil of copper wire. The water reservoir controlled the temperature of the thermistor and coil of copper wire, and the wheatstone bridge was used for the coil of copper wire to record the current value on the standard decade resistance box and the number value on the ten turn potentiometer. These values were then used to calculate the resistance of the copper wire. A volt-ohm meter was connected directly to the thermistor to acquire the measurements required to calculate its resistance. These values were taken and calculated at many different temperatures as the devices were heated in order to form a conclusion about the relationship between temperature and resistance of a material. In addition, the of the thermistor was calculated to give a numerical representation of the ability of the electrons in the semiconducting material to bridge the band gap. Calculations: For the coil of copper wire, the ohm reading from the standard decade resistance box and the value on the ten turn potentiometer were recorded once the wheatstone bridge was balanced at each temperature. Upon recording these values in an Excel sheet, the value of resistance at each temperature could be calculated using the following equation. Our resistance values for the temperature range of 65 degrees Celsius to 70 degrees Celsius were inconsistent with the rest of the data. Therefore, we calculated the ? value for the entire data set; we concluded that even though the data seemed to deviate from the linear regression line the calculated ? was within the same order of magnitude as the given ? value for copper so our data was accurate enough. The percent error between our ? value and the one given was 55 percent, but if the outliers above 60 degrees Celsius were thrown out, the error percent went down to three percent. The ? value was calculated by For the thermistor, the resistance reading was taken directly from the volt-ohm meter that was attached to the thermistor. Since this already gave the resistance value of the thermistor, the other calculation that needed to be done was finding the of the entire data set, which was calculated using To find the slope of the graph, the natural log of resistance versus the inverse temperature in Kelvin was plotted. This part of the experiment seemed to have a better fitting linear regression line than the copper coil. Coil of Copper Wire Thermistor Conclusions: The experiment showed that the resistance of the copper wire increased linearly with a steady increase in temperature. The thermistor?s resistance, however, decreased as the temperature increased, but in order to see a linear relationship between the temperature and resistance the natural log of the resistance had to be plotted against the inverse of the temperature in Kelvin. Both of these conclusions were backed by both the graphical representation of the data and the mathematical analysis as a result of using the equations and theories already established. The percent error of 55 percent between the ? values for the copper coil was very large and needed to be looked at more closely. Upon further analysis of the data, it was observed that the percent error decreased substantially if the outliers were removed from the data. Even though there were some outliers in the copper coil data, the overall analysis showed an increase in the resistance as temperature increased. These outliers could be due to the fact that convection currents were created in the water bath as a result of uneven heating and not enough stirring. Overall, the predicted outcome of the experiment was witnessed and proven quantitatively. T (?C) n1 Rs (ohm) R 0 = 2.25025 ? = 0.00178R (ohm) 24.9 5.255 2 2.214963119 30 5.284 2 2.240882103 35 5.309 2 2.263483266 40 5.332 2 2.284490146 45 5.424 2 2.370629371 50 5.449 2 2.394638541 55 5.514 2 2.458314757 60 5.549 2 2.493372276 65 5.418 2 2.364906155 70 5.409 2 2.356349379 75 5.458 2 2.403346543 80 5.524 2 2.468275246 T (?C) R (ohm) T (K) 1/T (K?1) = 0.5987ln (R) 25.5 25.5 298.5 0.003350084 3.238678452 30 21.6 303 0.00330033 3.072693315 35 17.4 308 0.003246753 2.856470206 40 14.6 313 0.003194888 2.681021529 45 11.9 318 0.003144654 2.4765384 50 10 323 0.003095975 2.302585093 55 8.3 328 0.00304878 2.116255515 60 7.3 333 0.003003003 1.987874348 65 6.5 338 0.00295858 1.871802177 70 5.6 343 0.002915452 1.722766598 75 4.9 348 0.002873563 1.589235205 80 4.2 353 0.002832861 1.435084525