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Q28 (CDS-I/2017) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Electricity and magnetism Answer Verified

A copper wire of radius r and length I has a resistance of R. A second copper wire with radius 2r and length I 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

Result
Your answer: —  ·  Correct: D
Explanation

The resistance of a wire is given by the formula R = ρL/A, where ρ is resistivity, L is length, and A is the cross-sectional area [2]. Since the cross-sectional area of a wire is modeled as a circle (A = πr²), resistance is inversely proportional to the square of the radius [4]. The first wire has resistance R. The second wire has the same length and material but twice the radius (2r), making its area 4πr². Consequently, its resistance is R/4 [1]. When these two wires (R and R/4) are connected in parallel, the equivalent resistance (Rp) is calculated using the reciprocal sum formula: 1/Rp = 1/R + 1/(R/4). This simplifies to 1/Rp = 1/R + 4/R = 5/R. Therefore, the resultant resistance Rp is R/5.

Sources

  1. [2] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Example 11.6 > p. 180
  2. [4] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.6 > p. 186
  3. [1] Science , class X (NCERT 2025 ed.) > Chapter 11: Electricity > Activity 11.3 > p. 178
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