The following figure shows a circuit diagram. We can find the currents through and potential differences across different resistors using Kirchhoff's rules. Answer the following questions based on the above : (a) Which points are at the same potential in the circuit ? (b) What is the current through arm bg ? (c) Find the potential difference across resistance R_3. (c) What is the power dissipated in resistance R_2 ?

PhysicsCBSE Class 12 · Board exam 2023, set 55/1/1 · 4 marks · Case-based

CBSE Class 12 Physics 2023: question 34

Set in the CBSE Class 12 board exam of 2023, paper 55/1/1, section E, question 34, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q34 · 4 marks · Case-basedCompetency-basedCurrent Electricity

The following figure shows a circuit diagram. We can find the currents through and potential differences across different resistors using Kirchhoff's rules.

Answer the following questions based on the above :

(a)
Which points are at the same potential in the circuit ?
1 mark
(b)
What is the current through arm bg ?
1 mark
(c)
Find the potential difference across resistance $R_{3}$ .
2 marks
OR
(c)
What is the power dissipated in resistance $R_{2}$ ?
2 marks

Figure in the paper: Circuit with points a, b, c along top; h, g, f along bottom. Left arm a-h contains battery E = 6·0 V and internal resistance r = 1·0 $Ω$ . Middle arm b-g contains $R_{1}$ = 10 $Ω$ (points i and j at its ends). Right arm c-f contains $R_{2}$ = 5·0 $Ω$ then points d, e, then $R_{3}$ = 5·0 $Ω$ . Current arrows along a to b and b to c, and downward at b into the middle arm. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 55/1/1.

Hints

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

Hint 1

Points joined by plain wire (no resistor or cell between them) are at the same potential.

Hint 2

Use one current through the battery and another through R₁. The rest flows through R₂ and R₃. Apply the loop rule to two loops.

Hint 3

Once you know the current in the right-hand arm, use V = IR or P = I²R.

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) Points joined only by connecting wires of negligible resistance are at the same potential. The groups are:
- a, b, c (and i, the top end of $R_{1}$ );
- d and e;
- f, g, h and j (the bottom end of $R_{1}$ ).
1 mark
(b) Let $I_{1}$ be the current through the battery and $I_{2}$ the current through arm bg ( $R_{1}$ ). Then $(I_{1} - I_{2})$ flows through arm cf ( $R_{2}$ and $R_{3}$ in series, 10 Ω).
Loop abgha: $- 6 + 10 I_{2} + 1 \cdot I_{1} = 0 \Rightarrow I_{1} + 10 I_{2} = 6$ ...(i)
Loop acfha: $- 6 + 10 (I_{1} - I_{2}) + 1 \cdot I_{1} = 0 \Rightarrow 11 I_{1} - 10 I_{2} = 6$ ...(ii)
½ mark
Adding (i) and (ii): $12 I_{1} = 12$ , so $I_{1} = 1$ A.
Then from (i), $I_{2} = \frac{6 - 1}{10} = 0.5$ A.
Current through arm bg = 0.5 A.
½ mark
(c) [first alternative] The current through $R_{3}$ is $I_{1} - I_{2} = 1 - 0.5 = 0.5$ A.
$V_{R_{3}} = (I_{1} - I_{2}) R_{3} = 0.5 \times 5.0$
1 mark
$V_{R_{3}} = 2.5$ V
1 mark
(c) [second alternative] The current through $R_{2}$ is also 0.5 A.
$P = (I_{1} - I_{2})^{2} R_{2} = (0.5)^{2} \times 5.0 = 1.25$ W
(This alternative carries the same 2 marks as the first; only one is answered in the exam.)

Answer: (a) a, b, c (with i); d, e; f, g, h, j; (b) 0.5 A; (c) 2.5 V across R₃ / 1.25 W in R₂

Where the marks are

Identifies the groups of points at equal potential (1 mark)
Writes the two Kirchhoff loop equations (½ mark)
Solves to get I₁ = 1 A and I₂ = 0.5 A through bg (½ mark)
Uses V = (I₁ − I₂)R₃ (1 mark)
Gets 2.5 V (1 mark)
OR: P = (I₁ − I₂)²R₂ = 1.25 W (2 marks)

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 paper2023 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 2023: question 34

Hints

Step-by-step solution

Revise the chapter

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