Conductive putty can easily be formed into different shapes to investigate the effect of shape on electrical resistance. A student uses vernier calipers to measure the diameter of d of a uniform cylinder made of the putty. Suggest one problem with using calipers to make this measurement. Table 1 shows the caliper measurements made by a student. Show that the percentage uncertainty in d is about 2.4%. Assume that all the data are valid. The length of the cylinder is 71 ± 2 mm. Determine the uncertainty, in mm³, in the volume of the cylinder. A student is given some putty to form into cylinders. To find the resistance of a cylinder, metal discs are placed in contact with the ends of the cylinder and connected to a resistance meter. The student plots the graph shown in Figure 8. Determine ρ. State an appropriate SI unit for your answer.

A-Level AQA Physics Resistance & Resistivity: Conductive putty can easily be f

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

Question 3

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Conductive putty can easily be formed into different shapes to investigate the effect of shape on electrical resistance. A student uses vernier calipers to measure ... show full transcript

Worked Solution & Example Answer: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

Step 1

Suggest one problem with using calipers to make this measurement.

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Answer

Calipers may reduce the reading of the diameter due to incorrect alignment or pressure when taking the measurement.

Step 2

Show that the percentage uncertainty in d is about 2.4%. Assume that all the data are valid.

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Answer

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:

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

Step 3

Determine the uncertainty, in mm³, in the volume of the cylinder.

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Answer

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.

Step 4

Determine ρ. State an appropriate SI unit for your answer.

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Answer

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).

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

Worked Solution & Example Answer: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

Suggest one problem with using calipers to make this measurement.

Show that the percentage uncertainty in d is about 2.4%. Assume that all the data are valid.

Determine the uncertainty, in mm³, in the volume of the cylinder.

Determine ρ. State an appropriate SI unit for your answer.

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