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A material B has twice the specific resistance of A. A circular wire made of B has twice the diameter of a wire made of A. Then for the two wires to have the same resistance, the ratio l_B/l_A of their respective lengths must be

Asked in JEE Main 2006 · Resistance of a wire and stretching

Answer: (1) 2

Step-by-step solution

R=(ρ l)/(π d²/4), so equal resistance needs (ρ_A l_A)/(d_A²)=(ρ_B l_B)/(d_B²).

(l_B)/(l_A)=(ρ_A)/(ρ_B)((d_B)/(d_A))²=1/2×4.

(l_B)/(l_A)=2.

Why the other options are wrong

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