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, find the ratio lb/la.

Solution
The solution of your fiirst query is provided below
 

Let (ρA, lA, rA, AA) and (ρB, lB, rB, AB) be specific resistances, lengths, radii and areas of wires A and B, respectively.
 

Resistance of A = RA =ρAlAπrA2Resistance of B = RB =ρBlBπrB2As givenρB = 2 ρArB = 2 rARA= RBThereforeρAlAπrA2 =ρBlBπrB2ρAlAπrA2 =2 ρAlBπ2 rA2lBlA =21
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