Question

What equal length of an iron wire and a copper-nickel alloy wire, each of $2\text{mm}$ diameter connected parallel to give an equivalent resistance of $3\Omega$ ?
(Given resistivities of iron and copper-nickel alloy wire are $12\mu \Omega \text{cm}$ and $51\mu \Omega \text{cm}$ respectively)

• A. $110\text{m}$
• B. $82\text{m}$
• C. $97\text{m}$
• D. $90\text{m}$

Answer 1

The correct option is C $97\text{m}$

In the question the diameter and length of both the wires is same, and they are connected parallel to each other. Then, the effective resistance can be calculated as,

Using, $R=\rho \frac{l}{A}$
$R=\frac{\left({\rho }_1{\rho }_2\right)\frac{l^2}{A^2}}{({\rho }_1+{\rho }_2)\frac{l}{A}}$

i.e. $3=\frac{12\times 51}{12+51}\frac{l}{A}$

So we get the required length of the wires as,

$l=3\times \frac{63\times \pi \times (1{)}^2\times {10}^{-6}}{612}$

This gives $l=97\text{m}$