An electric cable of copper has just one wire of radius 9 mm. Its resistance is 14 Ω. If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius 3 mm connected in parallel, then the new resistance of the combination will be :

Solution

Physics sir · 3 steps

The length stays the same, so only the cross-section changes. Find one thin wire, then put seven in parallel.

1. Resistance and area. For a wire, R = (ρ L)/(π r²). The material and the length do not change, so R ∝ 1/r².
2. One thin wire. The radius drops from 9 mm to 3 mm, a factor of 3. The area therefore drops by a factor of 9, so one thin wire has resistance 9 × 14 = 126 Ω.

   R_(eq) = (126 Ω)/7 = 18 Ω

3. So. Seven identical 126 Ω wires in parallel give 18 Ω, which is option (b).

The idea to keep. For wires of the same length and material, R ∝ 1/r². Equal resistors in parallel give R/n. As a check, the combined area here is 7 × 9 = 63 mm² instead of 81 mm².

Answer from the NTA final answer key. Solution by PrepWiser.