A student measures the radius r and the resistance R of several equal lengths of wire. The results are shown in Table P2.5. It is suggested that R and r are related by the equation:

R = ar^b

Where a and b are constants.

a. A graph is plotted with ln R on the y-axis and ln r on the x-axis. Express the gradient and y-intercept in terms of a and b.

b. Values of r and R measured in an experiment are given in Table P2.5.

Copy and complete the table by calculating and recording values of ln (r/mm) and ln (R/Ω) and include the absolute uncertainties in ln (r/mm).

c. Plot a graph of ln (r/mm) against ln (R/Ω). Include error bars for ln (r/mm).

d. Draw the line of best fit and a worst acceptable straight line on your graph.

e. Determine the gradient of the line of best fit. Include the uncertainty in your answer.

f. Using your answer to part e, determine the value of b.

g. Determine the value of a and its uncertainty.

Transcribed Image Text:

r/ mm R/2 In r/ mm In R/ 2 2.0 0.1 175.0 3.0 ± 0.1 77.8 4.0 ± 0.1 43.8 5.0 0.1 28.0 6.0 0.1 19.4