Question

A wire of length $5\text{m}$ and radius $1\text{mm}$ has resistance of $1\Omega$. What length of the same material at the same temperature, and of radius $2\text{mm}$ will also have a resistance of $1\Omega$ ?

• A. $1.25\text{m}$
• B. $2.5\text{m}$
• C. $10\text{m}$
• D. $20\text{m}$

Answer 1

The correct option is D $20\text{m}$

$R=\rho \frac{l}{A}$

$R_1={\rho }_1\frac{l_1}{A_1}={\rho }_2\frac{l_2}{A_2}=R_2$
Material is same,
${\rho }_1={\rho }_2$
$⟹\frac{l_1}{\pi r_1^2}=\frac{l_2}{\pi r_2^2}$
$⟹\frac{5}{(1{)}^2}=\frac{l_2}{(2{)}^2}$
$⟹l_2=20m$