Conductive putty can easily be formed into different shapes to investigate the effect of shape on electrical resistance - AQA - A-Level Physics - Question 3 - 2022 - Paper 3

To calculate the average diameter:

d_{avg} = rac{34.5 + 32.9 + 33.4 + 34.0 + 34.0}{5} = 33.44 ext{ mm}

The range is from 32.9 mm to 34.5 mm, so:

ext{uncertainty} = rac{34.5 - 32.9}{2} = 0.8 ext{ mm}

Percentage uncertainty is calculated as:

ext{Percentage Uncertainty} = rac{0.8 ext{ mm}}{33.44 ext{ mm}} imes 100 \\ ext{Percentage Uncertainty} hickapprox 2.39\\ ext{or about } 2.4\%

The volume V of a cylinder is given by:

V = rac{ heta}{4} imes h

Using $d = 71 ext{ mm}$ and $h = 71 ext{ mm}$:

ext{uncertainty in volume} = V imes rac{( ext{uncertainty in } d)}{d} + V imes rac{( ext{uncertainty in } h)}{h}

This requires calculating the volumes based on the given uncertainties.

Using the formula:

$R = \frac{\rho L}{A} \\\ ext{where } L = ext{length}, A = \pi \left(\frac{d}{2}\right)^2$

The resistivity ρ can be determined from the slope of the graph plotted. From the graph, calculate the gradient. The appropriate SI unit for resistivity is ohm-meter (Ω·m).