Capacitor Questions

Q7. A student was required to design an experiment to measure the acceleration of a heavy cylinder as it rolled down an inclined slope of constant gradient. He suggested an arrangement that would make use of a capacitor-resistor discharge circuit to measure the time taken for the cylinder to travel between two points on the slope.

The principle of this arrangement is shown in the diagram below.

S1 and S2 are two switches that would be opened in turn by plungers as the cylinder passed over them. Once opened, the switches would remain open. The cylinder would be released from rest as it opened S1. The pd across the capacitor would be measured by the voltmeter.

(a) Describe the procedure the student should follow, including the measurements he should make, when using this arrangement. Explain how he should use the measurements taken to calculate the acceleration of the cylinder down the slope.

Your writing should be legible and the spelling, punctuation and grammar should be sufficiently accurate for the meaning to be clear.

Your answer will be assessed holistically.

That means the examiner will read it thorugh to see how 'it feels', whether you explain yourself well. The answer will then be assigned to one of the three levels according to the following criteria.

High Level (good to excellent) 5 or 6 marks

To get this level the information conveyed by the answer must be clearly organised, logical and coherent, using appropriate specialist vocabulary correctly. The form and style of writing must be appropriate to answer the question.

You have to provide a comprehensive and logical description of the sequence of releasing the ball and taking measurements of initial and final voltages. You should identify the correct distance measurement and show a good appreciation of how to use these measurements to calculate the time and acceleration from them. Time should be found from capacitor discharge, using known C and R values.

Repeated readings would be expected in any answer worthy of full marks, but five marks may be awarded where repetition is omitted.

Intermediate Level (modest to adequate) 3 or 4 marks

The information conveyed by the answer may be less well organised and not fully coherent. There is less use of specialist vocabulary, or specialist vocabulary may be used incorrectly. The form and style of writing is less appropriate.

You would provide a comprehensive and logical description of the sequence of releasing the ball and taking measurements of the initial and final voltages and perhaps show some appreciation of the use of suvat equations to calculate the acceleration, but you may not have mentioned the need to measure a distance.

Low Level (poor to limited) 1 or 2 marks

The information conveyed by the answer is poorly organised and may not be relevant or coherent. There is little correct use of specialist vocabulary. The form and style of writing may only be partly appropriate. The candidate is likely to have recognised that initial and final voltages should be measured, but may not appreciate the need for any other measurement. You may present few details of how to calculate the acceleration from the voltage measurements.

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The explanation expected in a competent answer should include a coherent selection of the following points.

Measurements

● initial pd across C (V₀) from voltmeter (before releasing roller)

● distance 's' along slope between plungers using a metre rule or tape

● final pd across C (V₁) from voltmeter

● measurements repeated to provide a more reliable result

Analysis

● time t is found from V₁ = V₀e^-t/RC, giving t = RC ln (V₀/V₁)

● Using Newton's equations of motion s = ut + ½ at² where u = 0, therefore acceleration a = 2s/t²

● repeat and find average 'a' from several results OR finding t for several different values of s you could plot a graph of t² against s. the gradient of the graph would be equal to 2/a

(6 marks)

(b) When the student set up his experiment using the arrangement shown above, he used a 22 μF capacitor, C, and a 200 kΩ resistor, R. In one of his results, the initial pd was 12.0 V and the final pd was 5.8V. The distance between the plungers was 2.5 m.

(i) From the student's result, calculate the time taken for the cylinder to reach the second plunger.

RC = 22 × 10–⁶ × 200 × 10³

RC = 4.40 = 4.4 s

V₁ = V₀e^-t/RC

t = RC ln (V₀/V₁)

t = 4.40 ln (12.0/5.8)

t = 3.2 s

(3 marks)

(ii) What value does this result give for the acceleration, in ms^-2, of the cylinder down the slope, assuming the acceleration is constant?

s = ut + ½ at²

where u = 0,

therefore acceleration a = 2s/t²

a = (2 x 2.5)/(3.2)²

a = 0.49 m s–^-2

(2 marks)

(Total 11 marks)