A student investigates an electrical circuit. The circuit is set up as shown in Fig. 2.1. A battery of negligible internal resistance is connected to a resistor of resistance $$\(Z\)$$. Five resistors, each of resistance $$\(R\)$$, are connected in parallel between P and Q . The switch is closed. The total current $$\(I\)$$ in the circuit is measured using the ammeter. The experiment is then repeated by changing the number $$\(n\)$$ of resistors, each of resistance $$\(R\)$$, connected in parallel between P and Q . It is suggested that $$\(I\)$$ and $$\(n\)$$ are related by the equation $$\[ E=I\left(\frac{R}{n}+Z\right) \]$$ where $$\(E\)$$ is the electromotive force (e.m.f.) of the battery. The experiment is repeated with 20 resistors, each of resistance $$\(R\)$$, connected in parallel between P and Q . Determine the total current $$\(I\)$$ in the circuit. $$\[ I= \]$$ A
Exam No：9702_s25_qp_51 Year：2025 Question No：2(e)
Answer:
Knowledge points:
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
Solution:
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