Question

A $1m$ long wire of diameter of $0.31mm$ has a resistance of $4.2ohms$ . If it is replaced by another wire of same material of length $1.5m$ and diameter $0.155mm,$ 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, $R_1=4.2\Omega ,$
$l_1=1m,A_1=\pi r_1^2=\pi {\left(\frac{0.31}{2}\right)}^2$
$R_2=?,I_2=1.5A_2=\pi r_2^2$
$=\pi {\left(\frac{0.155}{2}\right)}^2$
$\therefore \frac{4.2}{R}=\frac{1}{\pi (0.31{)}^2}\times \frac{\pi (0.155{)}^2}{1.5}$
$\Rightarrow R=\frac{4.2\times 0.31\times 0.31\times 1.5}{0.155\times 0.155}$
$=25.2\Omega$