Project 5
Linear Regression:
Internal Resistance of a Test Cell
Chapter 28,
Physics for Scientists and Engineers by Fishbane, Gasiorowicz,
and Thornton
INTRODUCTION
A onemeter slide wire potentiometer has been calibrated using a
standard cell. This potentiometer has been used to measure the emf
of a test cell. The terminal voltage of the same test cell is then
measured as different load resistors are connected across the test
cell. These data are used to determine the internal resistance of
the test cell.
Three sets of data were obtained. For each set, the following
values of load resistors, R, were:

150, 100, 60, 30, 15, 10, 8, 6, and 4 ohm.
For the three sets of data, the measured voltages, V, were as follows:

1.467, 1.466, 1.465, 1.457, 1.442, 1.428, 1.416, 1.401, and 1.369 V.

1.261, 1.273, 1.255, 1.251, 1.228, 1.203, 1.183, 1.150, and 1.105 V.

1.525, 1.523, 1.517, 1.498, 1.466, 1.446, 1.418, 1.403, and 1.340 V.
A linear least squares analysis using the MATLAB program,
p23best1, will
yield information about the degree to which these data fit a straight
line. The procedure for measuring the voltage across the load
resistor and the corresponding circuit diagram is shown in the manual
for the experiment
P23 The Potentiometer: Internal Reistance of a Test Cell.
EXERCISES
 Using the three sets of data, plot graphs with terminal voltage
V on the vertical axis and current, I on the horizontal axis.
 Draw the best fit straight line through each set of data points.
 Run the program,
p23best1, and report the results for the three sets of data
shown above.
 For each case, determine the internal resistance of the test cell from
the best fit parameters.
 Modify the program,
p23best1,
to calculate the chisquare function for each
case. How do these
values of chisquare compare with N  M, where
N is the number of data points and M is the number
of parameters used in the fit.
LINKS
SOME REFERENCES FROM ABOVE
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