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प्रश्न
What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3 Ω?
(Given resistivities of iron and copper-nickel alloy wire are 12 µΩ cm and 51 µΩ cm respectively).
पर्याय
82 m
110 m
97 m
90 m
MCQ
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उत्तर
97 m
Explanation:
Given that the dimensions of both wires are the same.
i.e., lCu-Ni = lFe = l and AFe = ACu-Ni = πr2
From the relation, R = `rhol/A`, ρ-Resistivity.
Given ρFe = 12 µΩ cm, ρCu-Ni = 15 µΩ cm, Req. = 3Ω
`1/R_{eq} = 1/R_{Fe} + 1/R_{Cu-Ni}`
⇒ `1/3 = A/(rho_{Fe}l) + A/(rho_{CuNi}l)`
`l = 3A(1/(rho_{Fe}) + 1/(rho_{Cu-Ni}))`
= `3pir^2((rho_{Fe} + rho_{Cu-Ni})/(rho_{Fe} xx rho_{Cu-Ni}))`
`l = 3pi xx (1 xx 10^-3)^2[(12 + 51)/(12 xx 51)]`
= 97 m
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