ScienceCBSE Class 10 · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 10 Science sample paper 2023-24: question 25(a)

From the official CBSE sample question paper for 2023-24, section B, question 25(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(a) · 2 marks · Very short answerElectricity

A piece of wire of resistance R is cut into three equal parts. These parts are then connected in parallel. If the equivalent resistance of this parallel combination is $R_{1}$ , what is the value of the ratio $R_{1} : R$ ?

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

How does the resistance of a wire change when its length becomes one-third?

Hint 2

Use $\frac{1}{R _{p}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \frac{1}{R _{3}}$ with each piece equal to R/3.

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.

Resistance is directly proportional to length ( $R \propto l$ ). Each of the three equal parts therefore has resistance $\frac{R}{3}$ .
½ mark
For three resistors in parallel: $\frac{1}{R _{1}} = \frac{1}{R /3} + \frac{1}{R /3} + \frac{1}{R /3} = \frac{3}{R} + \frac{3}{R} + \frac{3}{R} = \frac{9}{R}$
1 mark
So $R_{1} = \frac{R}{9}$ , which gives $\frac{R _{1}}{R} = \frac{1}{9}$ , i.e. $R_{1} : R = 1 : 9$ .
½ mark

Answer: $R_{1} : R = 1 : 9$

Where the marks are

Each part has resistance $R /3$ , because resistance is proportional to length (0.5 mark)
Correct parallel formula giving $1/ R_{1} = 9/ R$ (1 mark)
Final ratio $R_{1} : R = 1 : 9$ (0.5 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 paperSample paper 2023-24: every question, by section.

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CBSE Class 10 Science sample paper 2023-24: question 25(a)

Hints

Step-by-step solution

Revise the chapter

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