What equal length of an iron wire and a copper-nickel alloy wire, each of 2mm diameter connected parallel to give an equivalent resistance of 3 $Ω$ ?

(Given resistivities of iron and copper-nickel alloy wire are $12 μ Ω$ cm and 51 $μ Ω$ cm respectively)

Option 1 - 110m

Option 2 - 90m

Option 3 - 82m

Option 4 - 97m

3 Views|Posted 6 months ago

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Vishal Baghel | Contributor-Level 10

6 months ago

Correct Option - 4

Detailed Solution:

$\frac{R_{1} R_{2}}{R_{1} + R_{2}} = 3$

$\Rightarrow \frac{(ρ_{1} \frac{l}{A}) (ρ_{2} \frac{l}{A})}{(\frac{ρ_{1} l}{A}) + (\frac{ρ_{2} l}{A})} = 3$

$= \frac{3 * [\frac{π}{4} * {(2 * 1 0^{- 3})}^{2}] [12 + 51] * 1 0^{- 6} * 1 0^{- 2}}{12 * 1 0^{- 6} * 1 0^{- 2} * 51 * 1 0^{- 6} * 1 0^{- 2}}$

$= 97$

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What equal length of an iron wire and a copper-nickel alloy wire, each of 2mm diameter connected parallel to give an equivalent resistance of 3 Ω ? (Given resistivities of iron and copper-nickel alloy wire are 1 2 μ Ω cm and 51 μ Ω cm respectively)

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