Question

A nichrome wire $ 50\, cm $ long and $ 1 \,mm^2 $ 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

Answer: (A)

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