To check the resistance of a sample wire

PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

To check the resistance of a sample wire, a student must calculate

R=\dfrac{\rho l}{\pi r^{2}}

. The following measurements were made: • Resistivity

\rho=(1.72\,\pm0.02)\times10^{-8}\,\Omega\,\text{m}

• Length

l=(1.000\,\pm0.002)\,\text{m}

• Radius

r=(0.500\,\pm0.005)\,\text{mm}

(i) Compute the resistance

R

and its percentage uncertainty. Express

R

with the correct significant figures. (ii) Determine the individual percentage contributions of the uncertainties in

\rho

l

and

r

to the total percentage uncertainty in

R

. (iii) If only one of the three measurements could be improved, which should be chosen to reduce the overall percentage uncertainty in

R

to roughly half its present value? Support your answer with a quantitative argument.