Question

A nichrome wire 50 cm long and 1 mm cross-section carries a current of 4 A when connected to a 2 V battery. The resistivity of nichrome wire is

• A. $1\times {10}^{-6}\Omega -m$
• B. $4\times {10}^{-7}\Omega -m$
• C. $3\times {10}^{-7}\Omega -m$
• D. $2\times {10}^{-7}\Omega -m$

Answer 1

The correct option is A $1\times {10}^{-6}\Omega -m$

Here, l=50 cm = 0.5 m
and $A=1{mm}^2={10}^{-6}{m}^2$
As $R=\frac{V}{i}=\frac{pl}{A}$
$\Rightarrow p=\frac{VA}{il}$
$=\frac{2\times {10}^{-6}}{4\times 0.5}={10}^{-6}\Omega -m$
$=1\times {10}^{-6}\Omega -m$