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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 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

Result
Your answer: —  ·  Correct: A

Explanation

The resistance (R) of a wire is given by the formula R = ρl/A, where ρ is the resistivity, l is the length, and A is the cross-sectional area (A = πr²). This formula shows that resistance is inversely proportional to the square of the radius (R ∝ 1/r²).

  • First Wire: Has a radius r and resistance R.
  • Second Wire: Has a radius 2r. Since the radius is doubled, the area increases by 4 times (2²), making its resistance R/4.

When these two wires are connected in parallel, the equivalent resistance (Rp) is calculated as:

1/Rp = 1/R + 1/(R/4)
1/Rp = 1/R + 4/R = 5/R

Inverting the equation, we get Rp = R/5.

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