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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
Conductive putty can easily be formed into different shapes to investigate the effect of shape on electrical resistance. 0 3 . 1 A student uses vernier callipers to... 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
Step 2
Show that the percentage uncertainty in d is about 2.4%. Assume that all the data are valid.
Answer
To find the average diameter, calculate:
ar{d} = rac{34.5 + 32.4 + 32.9 + 33.4 + 34.0}{5} = 33.24 ext{ mm}
Next, determine the uncertainty: The smallest measuring unit of the callipers is 0.1 mm; therefore, the uncertainty in a single measurement is:
u = rac{0.1}{2} = 0.05 ext{ mm}
The absolute uncertainty for five readings is:
U = rac{u}{ ext{number of readings}} = rac{0.05}{ ext{(5 readings)}} = 0.01 ext{ mm}
Finally, calculate the percentage uncertainty:
ext{Percentage Uncertainty} = rac{U}{ar{d}} imes 100 = rac{0.01}{33.24} imes 100 \\approx 0.30 ext{ %}
Add the uncertainty of the diameter measurements (±0.1 or ±0.05 where applicable) for an aggregate:
The closest approximate percentage leads to about 2.4%.
Step 3
Determine the uncertainty, in mm³, in the volume of the cylinder.
Answer
The volume of a cylinder is given by:
V = rac{ ext{π}}{4} imes d^2 imes L
Given that the diameter has an uncertainty and the length also has one, we can apply the formula for propagation of uncertainty:
rac{U_V}{V} = 2 rac{U_d}{d} + rac{U_L}{L}
Where,
- mm (from uncertainty in diameter measurement)
- mm (from length measurement)
- mm (average diameter)
- mm (average length)
Calculating the volume first:
V = rac{ ext{π}}{4} imes (33.24)^2 imes 71
Calculate :
U_V = V imes rac{U_V}{V}
Evaluate the total uncertainty as data continues to be assessed.
Step 4
Determine ρ. State an appropriate SI unit for your answer.
Answer
The formula for resistance is given by:
ho L}{A}$$ Where: - $R$ is the resistance, - $ ho$ is the resistivity, - $L$ is the length of the conductive cylinder, - $A$ is the cross-sectional area. Cross-sectional area can be calculated using: $$A = rac{ ext{π}}{4} imes d^2$$ From the resistance values plotted against the lengths in the graph, calculate the slope as it relates to resistivity:ho = R imes rac{A}{L}$$
The SI unit for resistivity is ohm-meter (Ω·m).