When a wire is stretchedand its radius becomes r/2, then its resistance R will be.....................?
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L1A1 = L2A2 = V………………(1)
ρL1/A1 = R1or R1 = ρL1A1/A1^2 = ρV/A1^2………..….(2)
similarly, R2 = ρV/A2^2……………………………..(3)
dividing (2) on (3): R1/R2 = ρV/A1^2/ ρV/A2^2
⇨ R1/R2 = A2^2/A1^2 = (A1/A2)^2 = (πr1^2/ πr2^2)^2 = (r1^2/ r2^2)^2
⇨ R1/R2 = (r1^2/ r2^2)^2 let r2 = r1/2, so R1/R2 = (r1^2/ r1^2/2^2)^2 = 1/4^2
⇨ R1/R2 = 1/4^2⇨R2 = 4^2R1 = 16R1.
ρL1/A1 = R1or R1 = ρL1A1/A1^2 = ρV/A1^2………..….(2)
similarly, R2 = ρV/A2^2……………………………..(3)
dividing (2) on (3): R1/R2 = ρV/A1^2/ ρV/A2^2
⇨ R1/R2 = A2^2/A1^2 = (A1/A2)^2 = (πr1^2/ πr2^2)^2 = (r1^2/ r2^2)^2
⇨ R1/R2 = (r1^2/ r2^2)^2 let r2 = r1/2, so R1/R2 = (r1^2/ r1^2/2^2)^2 = 1/4^2
⇨ R1/R2 = 1/4^2⇨R2 = 4^2R1 = 16R1.
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