A student investigates a circuit containing capacitors. The circuit is connected with a capacitor of capacitance $$$A$$$, as shown in Fig. 2.1. Two capacitors, each of capacitance $$$C$$$, are connected in parallel between $$$P$$$ and $$$Q$$$. Initially, switch X and switch Z are closed and switch Y is open. Switches X and Z are opened. Switch Y is then closed. The maximum potential difference between $$$P$$$ and $$$Q$$$ is measured using the voltmeter. This procedure is repeated and the mean maximum potential difference $$$V$$$ between $$$P$$$ and $$$Q$$$ is determined. The experiment is then repeated by changing the number $$$n$$$ of capacitors, each of capacitance $$$C$$$, connected in parallel between P and Q . It is suggested that $$$V$$$ and $$$n$$$ are related by the equation $$\[ E A=V(n C+A) \]$$ where $$$E$$$ is the electromotive force (e.m.f.) of the battery. （d）（i）Using your answers to（a），（c）（iii）and（c）（iv），determine the values of $$$E$$$ and $$$C$$$ ．Include appropriate units． Data：$$$A=(2.2 \pm 0.2) \mathrm{mF}$$$ $$\[ \begin{aligned} & E=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \\ & C=\ldots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \end{aligned} \]$$ ［2］（ii）Determine the percentage uncertainty in your value of $$$C$$$ ． percentage uncertainty = .....................................................\%

Physics

IGCSE&ALevel

CAIE

Exam No：9702_s25_qp_52 Year：2025 Question No：2(d)

Answer:

Knowledge points:

1.3.1 understand that the avogadro constant Na is the number of atoms in 0.012kg of carbon-12

1.3.2 use molar quantities where one mole of any substance is the amount containing a number of particles equal to the avogadro constant Na

10.1.1 recall and use appropriate circuit symbols as set out in the ASE publication Signs, Symbols and Systematics (example circuit symbols are given in Section 5.5.)

10.1.2 draw and interpret circuit diagrams containing sources, switches, resistors, ammeters, voltmeters, and/or any other type of component referred to in the syllabus

10.1.3 define electromotive force (e.m.f.) in terms of the energy transferred by a source in driving unit charge round a complete circuit

10.1.4 distinguish between e.m.f. and potential difference (p.d.) in terms of energy considerations

10.1.5 understand the effects of the internal resistance of a source of e.m.f. on the terminal potential difference

10.2.1 recall Kirchhoff’s first law and appreciate the link to conservation of charge

10.2.2 recall Kirchhoff’s second law and appreciate the link to conservation of energy

10.2.3 derive, using Kirchhoff’s laws, a formula for the combined resistance of two or more resistors in series

10.2.4 solve problems using the formula for the combined resistance of two or more resistors in series

10.2.5 derive, using Kirchhoff’s laws, a formula for the combined resistance of two or more resistors in parallel

10.2.6 solve problems using the formula for the combined resistance of two or more resistors in parallel

10.2.7 apply Kirchhoff’s laws to solve simple circuit problems

19.1.1 define capacitance and the farad, as applied to both isolated conductors and to parallel plate capacitors

19.1.2 recall and use C = $\frac{Q}{V} $

19.1.3 derive, using the formula , conservation of charge and the addition of potential differences, formulae for combined capacitance for capacitors in series and in parallel

19.1.4 solve problems using the capacitance formulae for capacitors in series and in parallel

19.2.1 deduce, from the area under a potential-charge graph, the equation and hence

Answer:

Knowledge points:

Solution:

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