JEE Main · 2006 · 30 Apr 2006 · Offline · Current Electricity

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_{A} / ℓ_{B}

of their respective lengths must be

(A)2
(B)1
(C) $\frac{1}{2}$ ✓ Correct
(D) $\frac{1}{4}$

Answer: (C)

Solution

Resistance R = ρℓ/A with cross-section A = π(d/2)². Here ρ_B = 2ρ_A and d_B = 2d_A, so A_B = 4A_A. For equal resistance, ρ_Aℓ_A/A_A = ρ_Bℓ_B/A_B = 2ρ_Aℓ_B/(4A_A), which gives ℓ_A = ℓ_B/2. Therefore ℓ_A/ℓ_B = 1/2 → option C. The source key (2) is actually the inverse ratio ℓ_B/ℓ_A; the question asks ℓ_A/ℓ_B, so the correct choice is 1/2.

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option

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