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Science — CBSE Class 10 board question

Q1. [5]
Answer the following about electrical resistivity :
  1. (i) Write the relation between resistance R and electrical resistivity ρ of the material of a conductor in the shape of cylinder of length l and area of cross-section A. Hence derive the SI unit of electrical resistivity.
  2. (ii) The resistance of a metal wire of length 3 m is 60 Ω. If the area of cross-section of the wire is 4×10⁻⁷ m², calculate the electrical resistivity of the wire.
  3. (iii) State how would electrical resistivity be affected if the wire (of part 'ii') is stretched so that its length is doubled. Justify your answer.
Previously asked in CBSE board exam
2024 31/1/1 Q36(B)
Generated by claude-sonnet-4-6 · 2026-06-15 06:46 · grounding rag
Model Answer

(i) The relation between resistance and resistivity is:

$$R = \rho \frac{l}{A}$$

Rearranging: $\rho = \dfrac{RA}{l}$

SI unit of $\rho = \dfrac{\Omega \times m^2}{m} = $ Ω m

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(ii) Given: $l = 3$ m, $R = 60\ \Omega$, $A = 4 \times 10^{-7}$ m²

$$\rho = \frac{RA}{l} = \frac{60 \times 4 \times 10^{-7}}{3} = \frac{240 \times 10^{-7}}{3}$$

$$\boxed{\rho = 8 \times 10^{-6}\ \Omega\ \text{m}}$$

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(iii) Electrical resistivity will not change.

Resistivity is a characteristic property of the material, not of the shape or size of the conductor. Stretching doubles the length but also halves the area of cross-section, so the resistance changes (increases 4 times), but resistivity remains the same.

Source: Chapter 11, Section 11.5

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Explanation
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