PhysicsCBSE Class 12 · Board exam 2024, set 55/1/1 · 3 marks · Short answer

CBSE Class 12 Physics 2024: question 23(b)

Set in the CBSE Class 12 board exam of 2024, paper 55/1/1, section C, question 23(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q23(b) · 3 marks · Short answerCurrent Electricity

What is a Wheatstone bridge? Obtain the necessary conditions under which the Wheatstone bridge is balanced.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 55/1/1.

Hints

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

Hint 1

Draw four resistors in a diamond, with a cell on one diagonal and a galvanometer on the other.

Hint 2

'Balanced' means the galvanometer shows no current.

Hint 3

Apply Kirchhoff's loop rule to the two loops that contain the galvanometer, then put $I_{g} = 0$ .

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 Wheatstone bridge is an arrangement of four resistances forming a closed quadrilateral ABCD. A cell is connected across one diagonal (A and C) and a galvanometer of resistance G across the other (B and D). It is used to find an unknown resistance. Circuit (described): $R_{1}$ in arm AB, $R_{2}$ in BC, $R_{3}$ in AD and $R_{4}$ in DC.
1 mark
Let currents $I_{1}, I_{2}, I_{3}, I_{4}$ flow in $R_{1}, R_{2}, R_{3}, R_{4}$ and $I_{g}$ through the galvanometer from B to D. Kirchhoff's loop rule for loop ABDA: $- I_{1} R_{1} - I_{g} G + I_{3} R_{3} = 0$ ...(1)
½ mark
Loop rule for loop BCDB: $- I_{2} R_{2} + I_{4} R_{4} + I_{g} G = 0$ ...(2)
½ mark
The bridge is balanced when $I_{g} = 0$ . Then the junction rule at B and D gives $I_{2} = I_{1}$ and $I_{4} = I_{3}$ .
½ mark
From (1): $I_{1} R_{1} = I_{3} R_{3}$ . From (2): $I_{1} R_{2} = I_{3} R_{4}$ . Dividing, the balance condition is $\frac{R _{2}}{R _{1}} = \frac{R _{4}}{R _{3}}$ .
½ mark

Answer: Balanced when no current flows through the galvanometer, i.e. $\frac{R _{2}}{R _{1}} = \frac{R _{4}}{R _{3}}$

Where the marks are

Defines/describes the Wheatstone bridge with its circuit (1 mark)
Applies Kirchhoff's loop rule to the two loops (1 mark)
Uses $I_{g} = 0$ and the junction rule (½ mark)
Obtains $R_{2} / R_{1} = R_{4} / R_{3}$ (½ mark)

Revise the chapter

Chapter: Current Electricity (notes, formulas, where marks are lost and every past question)
Topic: Kirchhoff's Rules and Wheatstone Bridge

Practise this chapterBoard-style questions from Current Electricity, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 55/1/1: 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 12 Physics 2024: question 23(b)

Hints

Step-by-step solution

Revise the chapter

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