Questions & Answers

Q1a.
Short Answer 1 mark

Record the voltmeter reading E.

Model Answer:
E = voltmeter reading from Fig. 1.1
Explanation: The candidate must record the reading shown on the voltmeter.
Q1b.
Structured 1 mark

Set up the circuit shown in Fig. 1.2. The distance between F and G is L. Attach F and G to the wire so that L is approximately 30 cm. Close the switch. Record the value of L and the voltmeter reading V. Open the switch.

Model Answer:
L = approximately 30 cm; V = voltmeter reading for this setup
Explanation: This is an experimental measurement question; the expected response is the recorded values.
Q1c.
Structured 9 marks

Write down the value of E from (a). Increase L by changing the position of F on the wire. Record L and V and repeat until you have six sets of values of L and V. Include your values from (b). Record your results in a table. Include values of (E - V) / L in your table.

Model Answer:
A table of six sets of L and V values, including the calculated quantity (E - V) / L for each set.
Explanation: The answer depends on the student's experimental data.
Q1d(i).
Structured 3 marks

Plot a graph of (E - V) / L on the y-axis against V on the x-axis.

Model Answer:
A correctly plotted graph of (E - V) / L against V.
Explanation: The graph depends on the student's data.
Q1d(ii).
Structured 1 mark

Draw the straight line of best fit.

Model Answer:
A straight line of best fit drawn through the plotted points.
Explanation: This is a graphical construction based on the student's data.
Q1d(iii).
Short Answer 2 marks

Determine the gradient and y-intercept of this line.

Model Answer:
gradient = value from graph
Explanation: The gradient is determined from the student's best-fit line.
Model Answer:
y-intercept = value from graph
Explanation: The y-intercept is determined from the student's best-fit line.
Q1e.
Short Answer 2 marks

It is suggested that the quantities V and L are related by the equation (E - V) / L = PV - Q, where P and Q are constants. Using your answers in (d)(iii), determine the values of P and Q. Give appropriate units.

Model Answer:
P = gradient of the graph, with units of inverse resistance per length as appropriate from the axes
Explanation: Comparing with y = mx + c, P corresponds to the gradient.
Model Answer:
Q = negative y-intercept, with appropriate units from the graph
Explanation: Comparing with y = mx + c, -Q corresponds to the y-intercept.
Q1f.
Structured 1 mark

The resistance of R is R. Theory suggests that P and Q are both inversely proportional to R and the graph cuts the x-axis at a value of V = E/2 for all values of R. A student repeats the experiment using two identical resistors, each with a lower value of R than in the original experiment. For the student’s experiment, draw a second line on the graph to show the expected results. Label this line W.

Model Answer:
A second straight line labelled W with a larger gradient than the original line and the same x-intercept at V = E/2.
Explanation: Since P and Q are inversely proportional to R, lowering R increases the gradient and intercept magnitude, while the x-intercept remains fixed at E/2.
Q2a(i).
Short Answer 1 mark

The diameter of the smaller sphere is d, as shown in Fig. 2.1. Measure and record d.

Model Answer:
d = measured diameter of the smaller sphere
Explanation: This is an experimental measurement question.
Q2a(ii).
Short Answer 1 mark

Estimate the percentage uncertainty in your value of d. Show your working.

Model Answer:
percentage uncertainty = (absolute uncertainty in d / d) × 100%
Explanation: Percentage uncertainty is calculated from absolute uncertainty divided by the measured value.
Q2b(i).
Short Answer 1 mark

Set up the apparatus as shown in Fig. 2.2. Ensure that the rods are the same height above the bench. Slide the paper clips at the ends of the chain onto the rods. The distance between the centres of the rods is x. Position the stands so that x is approximately 70 cm. Measure and record x.

Model Answer:
x = approximately 70 cm; record the measured value
Explanation: This is an experimental measurement question.
Q2b(ii).
Short Answer 1 mark

Use the hook to attach the smaller sphere of modelling clay to the chain of paper clips as shown in Fig. 2.3. The number of paper clips between the hook and the end of the chain is n, as shown in Fig. 2.3. Place the hook so that n is 11. Calculate N, where N = n/23. Give your answer to three significant figures.

Model Answer:
N = 11/23 = 0.478
Explanation: Using the given formula N = n/23 with n = 11 gives 0.478 to three significant figures.
Q2c.
Short Answer 2 marks

Pull the sphere towards you through a short distance. When the sphere is released, it will oscillate. Take measurements to determine the period T of these oscillations.

Model Answer:
T = measured period of oscillation
Explanation: This is an experimental measurement question.
Q2d.
Structured 3 marks

Roll the two spheres into one larger sphere. Measure and record the diameter d of the larger sphere. Repeat (b) and (c) with a value x of approximately 80 cm and with the hook placed so that n is 7. Record x, N and T.

Model Answer:
d = measured diameter of the larger sphere; x = approximately 80 cm; N = 7/23 = 0.304; T = measured period
Explanation: This part requires experimental measurements and the calculation of N from n = 7.
Q2e(i).
Short Answer 1 mark

It is suggested that the relationship between T, d, N and x is T^2 = kdN/x^2, where k is a constant. Using your data, calculate two values of k.

Model Answer:
first value of k = T^2 x^2 / (dN)
Explanation: Rearranging the given equation gives k = T^2 x^2 / (dN).
Model Answer:
second value of k = T^2 x^2 / (dN)
Explanation: The same rearrangement is used for the second data set.
Q2e(ii).
Short Answer 1 mark

Justify the number of significant figures that you have given for your values of k.

Model Answer:
The number of significant figures should match the least precise measured quantity used in the calculation.
Explanation: Calculated values should be quoted to the precision justified by the least precise input measurement.
Q2f.
Short Answer 1 mark

It is suggested that the percentage uncertainty in the values of k is 15%. Using this uncertainty, explain whether your results support the relationship in (e).

Model Answer:
If the two values of k agree within 15% uncertainty, the results support the relationship; if not, they do not.
Explanation: Agreement within the stated uncertainty indicates consistency with the model.
Q2g(i).
Essay 4 marks

Describe four sources of uncertainty or limitations of the procedure for this experiment. For any uncertainties in measurement that you describe, you should state the quantity being measured and a reason for the uncertainty.

Model Answer:
Any four valid uncertainties or limitations, each with the measured quantity and reason where relevant.
Explanation: This is an open-response practical evaluation question.
Q2g(ii).
Essay 4 marks

Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.

Model Answer:
Any four valid improvements to the experimental method or apparatus.
Explanation: This is an open-response practical evaluation question.