Capacitors in Circuits (OCR A Level Physics)

The diagram below shows a circuit containing two capacitors which are both initially uncharged. The battery has e.m.f. E and negligible internal resistance.

The switch S is first moved to position A until the capacitor of capacitance C₀ is fully charged.

The switch S is then moved to position B. The initial charge stored by the capacitor of capacitance C₀ is shared between the two capacitors. The final reading on the voltmeter is V.

Show that

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A student wants to determine the values of E and C₀ by repeating the experiment above and measuring the potential difference (p.d.) V for a selection of capacitors of capacitance C.

The student decides to plot a graph of against C.

i) Use the expression in (a) to show that the graph should be a straight line of gradient and y-intercept .

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ii) The data points, error bars and the line of best fit drawn by the student are shown in the graph below.

The gradient of the line of best fit is 51 V^–1 F^–1. The value of E is 9.1 V.

Determine the value of C₀ in millifarads (mF). Write your answer to 2 significant figures.

C₀ = ..................................... mF [2]

iii) Draw on the graph a straight line of worst fit.

Use this line to determine the absolute uncertainty in your value of C₀. Write your answer to an appropriate number of significant figures.

absolute uncertainty = .................................... mF [4]

The experiment is repeated with a resistor of resistance 10 kΩ placed in series between S and the capacitor of capacitance C₀.

State with a reason what effect, if any, this would have on the experiment.

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