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Q72 (NDA-I/2026) Science & Technology › Basic Science (Physics, Chemistry, Biology)

Three wires each of length L, cross-sectional area A and resistivity p are connected as shown in the figure. These are to be replaced by another wire of same resistivity such that the resistance between points X and Z does not change. If L1 is the length and A1 is the cross-sectional area of the new wire, then which one among the following is correct?

Explanation

The resistance of a wire is given by the formula R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area. In the standard circuit configuration for this problem (two wires connected in parallel between points X and Y, and a third wire connected in series between Y and Z), the equivalent resistance (RXZ) is calculated as follows:

  • Resistance of each wire: R = ρL/A
  • Resistance of the parallel part (X to Y): Rp = (R × R) / (R + R) = R/2
  • Total resistance between X and Z: RXZ = Rp + R = R/2 + R = 3R/2 = 3ρL / 2A

The new wire must have the same resistance: Rnew = ρL1/A1 = 3ρL/2A. This condition is satisfied when L1 = 3L and A1 = 2A. Thus, option A is the correct choice.

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