Question

A $ 1\,m $ long wire of diameter of $ 0.31\,mm $ has a resistance of $ 4.2\,ohms $ . If it is replaced by another wire of same material of length $ 1.5\,m $ and diameter $ 0.155\,mm, $ the resistance of wire is

• A. 25.2 ohms
• B. 0.6 ohms
• C. 26.7 ohms
• D. 0.8 ohms

Answer 1

Answer: (A)

$R=\rho \frac{l}{A}$
Given, $R_{1}=4.2\, \Omega,$
$l_{1}=1\, m, A_{1}=\pi r_{1}^{2}=\pi\left(\frac{0.31}{2}\right)^{2}$
$R_{2}=?, I_{2}=1.5\, A_{2}=\pi r_{2}^{2}$
$=\pi\left(\frac{0.155}{2}\right)^{2}$
$\therefore \frac{4.2}{R}=\frac{1}{\pi(0.31)^{2}} \times \frac{\pi(0.155)^{2}}{1.5}$
$\Rightarrow R=\frac{4.2 \times 0.31 \times 0.31 \times 1.5}{0.155 \times 0.155}$
$=25.2\, \Omega$