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Science (086) — AI-generated practice question

AI-generated practice question — model-generated for extra practice, not a previous-year CBSE board question.

Q1. [1] medium thorough-understanding
Which of the following changes to a copper wire will reduce its resistance to one-quarter of its original value? (A) Halving its length and doubling its cross-sectional area (B) Doubling its length and halving its cross-sectional area (C) Halving both its length and cross-sectional area (D) Doubling both its length and cross-sectional area
  1. A Halving its length and doubling its cross-sectional area
  2. B Doubling its length and halving its cross-sectional area
  3. C Halving both its length and cross-sectional area
  4. D Doubling both its length and cross-sectional area
Generated by claude-sonnet-4-6 · 2026-06-26 01:10 · grounding rag
Model Answer

(A) Halving its length and doubling its cross-sectional area

Using $R = \rho \dfrac{l}{A}$: new resistance $= \rho \dfrac{l/2}{2A} = \dfrac{1}{4}\rho\dfrac{l}{A} = \dfrac{R}{4}$.

Source: Chapter 11, Section 11.5 (Example 11.6)

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Explanation

The formula $R = \rho \frac{l}{A}$ shows resistance is directly proportional to length and inversely proportional to area. Halving l gives factor ½; doubling A gives another factor ½ — together reducing R to ¼. This is directly solved in Example 11.6 of the textbook. For MCQs, always substitute the changes into the formula quickly to verify.

Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.