A student investigates a circuit containing capacitors. The circuit is connected with a capacitor of capacitance $$\(A\)$$, as shown in Fig. 2.1. Two capacitors, each of capacitance $$\(C\)$$, are connected in parallel between $$\(P\)$$ and $$\(Q\)$$. Initially, switch X and switch Z are closed and switch Y is open. Switches X and Z are opened. Switch Y is then closed. The maximum potential difference between $$\(P\)$$ and $$\(Q\)$$ is measured using the voltmeter. This procedure is repeated and the mean maximum potential difference $$\(V\)$$ between $$\(P\)$$ and $$\(Q\)$$ is determined. The experiment is then repeated by changing the number $$\(n\)$$ of capacitors, each of capacitance $$\(C\)$$, connected in parallel between P and Q . It is suggested that $$\(V\)$$ and $$\(n\)$$ are related by the equation $$\[ E A=V(n C+A) \]$$ where $$\(E\)$$ is the electromotive force (e.m.f.) of the battery. (b)Values of $$\(n\)$$ and the two measured values of the maximum potential difference $$\(V_{1}\)$$ and $$\(V_{2}\)$$ are given in Table 2.1. Calculate and record values of $$\(V / V\)$$ and $$\(\frac{1}{V} / V^{-1}\)$$ in Table 2.1.Include the absolute uncertainties in $$\(V\)$$ and $$\(\frac{1}{V}\)$$ . [2]

Physics
IGCSE&ALevel
CAIE
Exam No:9702_s25_qp_52 Year:2025 Question No:2(b)

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
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
19.3 Discharging a capacitor

Solution:

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