As shown in the diagram, an electric circuit consisting of an ammeter, a voltmeter, 4 cells of 1·5 V each, a plug key with a gap XY was set up. Voltmeter and ammeter readings were recorded in the observation table for four arrangements as given below :
Arrangement No. 1 – only resistor R₁ in gap XY
Arrangement No. 2 – only resistor R₂ in gap XY
Arrangement No. 3 – Resistors R₁ and R₂ in series in gap XY
Arrangement No. 4 – Resistors R₁ and R₂ in parallel in gap XY
Based on the observations, four V – I graphs A, B, C and D as shown in figure were drawn.
Read the following case and answer the questions that follow.
Generated by claude-sonnet-4-6 · 2026-06-15 06:43 · grounding stimulus
Model Answer
(a) Graph A represents the series combination of R₁ and R₂, because series combination gives the highest resistance, and the steepest slope in a V–I graph corresponds to the highest resistance.
(b) Graph D represents the parallel combination of R₁ and R₂, because parallel combination gives the lowest resistance, and the least steep slope in a V–I graph corresponds to the lowest resistance.
(c)(i) Connect two resistors in series (10 Ω + 10 Ω = 20 Ω), and then connect the third resistor (10 Ω) in parallel with this series combination.
$$R = \frac{20 \times 10}{20 + 10} = \frac{200}{30} = \frac{20}{3} \approx 6.67\ \Omega$$
(This gives 6.67 Ω, not 15 Ω.)
Correct arrangement: Connect two resistors in parallel first:
$$R_{parallel} = \frac{10 \times 10}{10 + 10} = 5\ \Omega$$
Then connect this parallel combination in series with the third resistor:
$$R_{total} = 5 + 10 = 15\ \Omega$$
Justification: Two 10 Ω resistors in parallel give 5 Ω; adding the third 10 Ω resistor in series gives 5 + 10 = 15 Ω.
Source: Chapter 11 – Electricity, Resistance in Series and Parallel combinations
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Explanation
- (a) & (b): In a V–I graph, slope = V/I = R. Steeper slope → higher R → series; gentler slope → lower R → parallel.
- (c): The key trick is two in parallel + one in series. Students often try series+parallel the other way — always verify with the formula. Examiners expect the diagram (draw two parallel branches each with 10 Ω, and one 10 Ω in series) and the numerical justification. Both parts earn the 2 marks.