Skip to content

In a metallic conductor, an… (Class 12 Physics 2025, Q29)

questionbuddy.in/q/cbse-12-physics-2025-55-7-1-q29-metallic-conductor-electron-moving-due

PhysicsCBSE Class 12 · Board exam 2025, set 55/7/1 · 4 marks · Case-based

CBSE Class 12 Physics 2025: question 29

Set in the CBSE Class 12 board exam of 2025, paper 55/7/1, section D, question 29, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 4 marks · Case-basedCompetency-basedCurrent Electricity

In a metallic conductor, an electron, moving due to thermal motion, suffers collisions with the heavy fixed ions but after collision, it will emerge out with the same speed but in random directions. If we consider all the electrons, their average velocity will be zero. When an electric field is applied, electrons move with an average velocity, known as drift velocity (). The average time between successive collisions is known as relaxation time (). The magnitude of drift velocity per unit electric field is called mobility ().
An expression for current through the conductor can be obtained in terms of drift velocity, number of electrons per unit volume (n), electronic charge (e), and the cross-sectional area (A) of the conductor. This expression leads to an expression between current density () and the electric field (). Hence, an expression for resistivity () of a metal is obtained. This expression helps us to understand increase in resistivity of a metal with increase in its temperature, in terms of change in the relaxation time () and change in the number density of electrons (n).

  1. (i)

    Consider two cylindrical conductors A and B, made of the same metal connected in series to a battery. The length and the radius of B are twice that of A. If and are the mobility of electrons in A and B respectively, then is :

    1. (A)
    2. (B)
    3. (C)2
    4. (D)1
    1 mark
  2. (ii)

    A wire of length 0·5 m and cross-sectional area m is connected to a battery of 2 V that maintains a current of 1·5 A in it. The conductivity of the material of the wire (in m) is :

    1. (A)
    2. (B)
    3. (C)
    4. (D)
    1 mark
  3. (iii)

    The temperature coefficient of resistance of nichrome is C. In order to increase resistance of a nichrome wire by 8·5%, the temperature of the wire should be increased by :

    1. (A)C
    2. (B)C
    3. (C)C
    4. (D)C
    1 mark
  4. (iv)(a)

    Consider the contribution of the following two factors I and II in resistivity of a metal :
    I. Relaxation time of electrons
    II. Number of electrons per unit volume
    The resistivity of a metal increases with increase in its temperature because :

    1. (A)I decreases and II increases.
    2. (B)I increases and II is almost constant.
    3. (C)Both I and II increase.
    4. (D)I decreases and II is almost constant.
    1 mark

  5. OR

    (iv)(b)

    A steady current flows in a copper wire of non-uniform cross-section. Consider the following three physical quantities :
    I. Electric field
    II. Current density
    III. Drift speed
    Then at the different points along the wire :

    1. (A)II and III change, but I is constant.
    2. (B)I and II change, but III is constant.
    3. (C)I and III change, but II is constant.
    4. (D)All I, II and III change.
    1 mark

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 55/7/1.

Hints

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

Hint 1

Recall the expressions μ = eτ/m, ρ = m/(ne²τ) and j = I/A.

Hint 2

For (ii) use σ = l/(RA) with R = V/I; for (iii) use ΔR/R = αΔT.

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.

  1. (i) Mobility depends only on the material (and temperature), not on the dimensions of the wire. Since A and B are of the same metal, . Option (D)

    1 mark

  2. (ii) . Option (C)

    1 mark

  3. (iii) C. Option (B)

    1 mark

  4. (iv)(a) . In a metal, n hardly changes with temperature, but more frequent collisions reduce . So I decreases and II is almost constant. Option (D)

    1 mark

  5. (iv)(b) I is the same everywhere, so changes with A. Then changes, and also changes. All three change. Option (D)

Answer: (i) D; (ii) C, 3.75 × 10⁶ Ω⁻¹ m⁻¹; (iii) B, 500 °C; (iv)(a) D; (iv)(b) D

Where the marks are

  • (i) μ_A/μ_B = 1, option D (1 mark)
  • (ii) σ = 3.75 × 10⁶ Ω⁻¹ m⁻¹, option C (1 mark)
  • (iii) ΔT = 500 °C, option B (1 mark)
  • (iv)(a) option D or (iv)(b) option D (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Current Electricity, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 55/7/1: 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.