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Q48 (CDS-II/2022) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Electricity and magnetism Answer Verified

A metal wire of length l and diameter d has a resistance R. What would be the resistance of another wire of the same metal and of the same length but having double the diameter?

Result
Your answer: —  ·  Correct: B

Explanation

The resistance (R) of a metallic conductor is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A), expressed as R = ρ(l/A) [2]. For a wire with a circular cross-section, the area is calculated as A = π(d/2)² or A = πd²/4, where d is the diameter. This implies that resistance is inversely proportional to the square of the diameter (R ∝ 1/d²). When the diameter of the wire is doubled (2d) while keeping the length and material constant, the new cross-sectional area increases by a factor of four (2² = 4). Since resistance is inversely proportional to this area, the new resistance becomes one-fourth of the original value (R/4). Therefore, doubling the diameter reduces the opposition to electron flow by providing four times the space, resulting in a resistance of R/4.

Sources

  1. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.3 > p. 178
  2. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > What you have learnt > p. 192
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SIMILAR QUESTIONS

NDA-I · 2019 · Q30 Relevance score: 6.89

Let us consider a copper wire having radius r and length l. Let its resistance be R. If the radius of another copper wire is 2r and the length is l/2 then the resistance of this wire will be

CDS-I · 2017 · Q28 Relevance score: 4.67

A copper wire of radius r and length l has a resistance of R. A second copper wire with radius 2r and length l is taken and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will be:

A) R/5
B) 5R/4
C) R/2
D) 4R/5

NDA-II · 2015 · Q43 Relevance score: 4.56

The resistance of a wire of length / and area of cross-section a is x ohm. If the wire is stretched to double its length, its resistance would become:

CDS-I · 2018 · Q33 Relevance score: 4.39

Two metallic wires made from copper have the same length, but the radius of wire 1 is half that of wire 2. The resistance of wire 1 is R. If both the wires are joined together in series, the total resistance becomes:

  • (A) 2R
  • (B) 1.25R
  • (C) 0.5R
  • (D) 1.33R

IAS · 2001 · Q100 Relevance score: 3.52

Two wires have their lengths, diameters and resistivities, all in the ratio of 1 : 2. If the resistance of the thinner wire is 10 ohms, the resistance of the thicker wire is