A wire of resistance R and length L is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be :

Solution

Physics sir · 3 steps

Cutting divides R by 5, and putting 5 equal pieces in parallel divides it by 5 again.

1. Resistance of one piece. For a wire of the same material and thickness, R = ρ L / A, so resistance is proportional to length. Each piece has length L/5, so each piece has resistance R/5.
2. Five in parallel. For n equal resistors r joined in parallel, the reciprocals add: 1/R_(eq) = n/r, so R_(eq) = r/n.

   R_(eq) = (R/5)/5 = R/25

3. So. The combined resistance is 1/25R, which is option (a).

The idea to keep. Cut a wire into n equal parts and join them in parallel, and the resistance becomes R/n²: one factor of n from the shorter length, one from the parallel combination.

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