Answer the following. (a) State Ohm's law. Write formula for the equivalent resistance R_p of the parallel combination of three resistors of values R_1, R_2 and R_3. (b) Find the resistance of the following network of resistors :

ScienceCBSE Class 10 · Board exam 2024, set 31/3/1 · 3 marks · Short answer

CBSE Class 10 Science 2024: question 33

Set in the CBSE Class 10 board exam of 2024, paper 31/3/1, section C, question 33, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q33 · 3 marks · Short answerElectricity

Answer the following.

(a)
State Ohm's law. Write formula for the equivalent resistance $R_{p}$ of the parallel combination of three resistors of values $R_{1}$ , $R_{2}$ and $R_{3}$ .
0 marks
(b)
Find the resistance of the following network of resistors :
0 marks

Figure in the paper: Resistor network between terminals X and Y: a resistor R in series from X, followed by two resistors R connected in parallel (one on the upper branch and one on the lower branch), then a wire to terminal Y. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 31/3/1.

Hints

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

Hint 1

Ohm's law relates V and I under one condition: which one?

Hint 2

First combine the two parallel resistors, then add the series one.

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) Ohm's law: The potential difference $V$ across the ends of a metallic conductor is directly proportional to the current $I$ through it, provided its temperature stays the same. So $V \propto I$ , i.e. $V = I R$ .
1 mark
(a) Parallel combination: $\frac{1}{R _{p}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \frac{1}{R _{3}}$
1 mark
(b) Parallel pair: The two resistors $R$ in parallel give $\frac{1}{R ^{'}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R}$ , so $R^{'} = \frac{R}{2}$ . This combination is in series with the first $R$ . Hence $R_{X Y} = R + \frac{R}{2} = \frac{3 R}{2}$ .
1 mark

Answer: (a) V ∝ I at constant temperature; 1/Rₚ = 1/R₁ + 1/R₂ + 1/R₃. (b) Equivalent resistance = 3R/2.

Where the marks are

Correct statement of Ohm's law including the constant-temperature condition (1 mark)
Correct parallel formula (1 mark)
Equivalent resistance R + R/2 = 3R/2 (1 mark)

Revise the chapter

Chapter: Electricity (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Electricity, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 31/3/1: every question, by section.

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CBSE Class 10 Science 2024: question 33

Hints

Step-by-step solution

Revise the chapter

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