ScienceCBSE Class 10 · Board exam 2025, set 31/3/1 · 4 marks · Case-based

CBSE Class 10 Science 2025: question 39

Set in the CBSE Class 10 board exam of 2025, paper 31/3/1, section E, question 39, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q39 · 4 marks · Case-basedCompetency-basedElectricity

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 $R_{1}$ in gap XY
Arrangement No. 2 – only resistor $R_{2}$ in gap XY
Arrangement No. 3 – Resistors $R_{1}$ and $R_{2}$ in series in gap XY
Arrangement No. 4 – Resistors $R_{1}$ and $R_{2}$ in parallel in gap XY

Based on the observations, four V – I graphs A, B, C and D as shown in figure were drawn. Study these graphs.

(a)
Which one of the graphs represents the series combination of $R_{1}$ and $R_{2}$ ?
1 mark
(b)
Which one of these graphs represents the parallel combination of $R_{1}$ and $R_{2}$ ?
1 mark
(c)(i)
Show an arrangement of three resistors, each of resistance $10 Ω$ , so that the combination has a resistance of $15 Ω$ . Give justification for your answer.
2 marks
OR
(c)(ii)
A battery of 6 V is connected with a series combination of five resistors of $0.1 Ω$ , $0.2 Ω$ , $0.3 Ω$ , $0.4 Ω$ and $0.5 Ω$ . How much current would flow through the $0.3 Ω$ resistor? Justify your answer.
2 marks

Figure in the paper: Left: circuit diagram with four cells (battery) connected in series, a plug key K, an ammeter A in the main line, and a voltmeter V connected across the gap between points X and Y, with resistors placed in gap XY. Right: V–I graph with axes I (amperes) on the vertical axis and V (volts) on the horizontal axis, all four straight lines starting from origin O: line A has the smallest slope, then B, then C, and D has the steepest slope. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 31/3/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

With I on the y-axis and V on the x-axis, what does the slope of each line represent?

Hint 2

Series increases the total resistance; parallel makes it smaller than the smallest resistor.

Hint 3

15 Ω = 10 Ω + 5 Ω: how can two 10 Ω resistors give 5 Ω?

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(a) The graphs have I on the y-axis and V on the x-axis, so slope $= \frac{I}{V} = \frac{1}{R}$ . The series combination has the largest resistance, so it has the smallest slope: Graph A.
1 mark
(b) The parallel combination has the least resistance (less than both $R_{1}$ and $R_{2}$ ), so it has the steepest slope: Graph D.
1 mark
(c)(i) Arrangement: connect two $10 Ω$ resistors in parallel, and connect this pair in series with the third $10 Ω$ resistor.
Parallel part: $R_{p} = \frac{R _{1} R _{2}}{R _{1} + R _{2}} = \frac{10 \times 10}{10 + 10} = 5 Ω$
1 mark
Total resistance: $R = R_{p} + R_{3} = 5 Ω + 10 Ω = 15 Ω$
1 mark
(c)(ii) (Alternative to (c)(i), also worth 2 marks.)
- Total resistance in series: $R_{s} = 0.1 + 0.2 + 0.3 + 0.4 + 0.5 = 1.5 Ω$
- Current: $I = \frac{V}{R _{s}} = \frac{6 V}{1.5 Ω} = 4.0$ A
- Justification: in a series circuit the same current flows through every resistor, so 4.0 A flows through the $0.3 Ω$ resistor.

Answer: (a) Graph A; (b) Graph D; (c)(i) two 10 Ω resistors in parallel (5 Ω) in series with the third 10 Ω gives 15 Ω; (c)(ii) 4.0 A, because the same current flows through all resistors in series.

Where the marks are

Graph A for series, with reasoning from slope = 1/R (1 mark)
Graph D for parallel (1 mark)
(c)(i) Correct arrangement and parallel value 5 Ω (1 mark)
(c)(i) Total 15 Ω shown (1 mark)
OR (c)(ii) R = 1.5 Ω and I = 6/1.5 = 4.0 A (1 mark)
OR (c)(ii) Justification: same current in series (1 mark)

Revise the chapter

Chapter: Electricity (notes, formulas, where marks are lost and every past question)
Topic: Resistors in Series and Parallel

Practise this chapterBoard-style questions from Electricity, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 31/3/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Science 2025: question 39

Hints

Step-by-step solution

Revise the chapter

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