Question

A nichrome wire 1m long and $1m{m}^2$ in crosssectional area draws $4$ ampere at $2$ volt. The resistivity of nichrome is

• A. $1\times {10}^{-7}nm$
• B. $2\times {10}^{-7}nm$
• C. $4\times {10}^{-7}nm$
• D. $5\times {10}^{-7}nm$

Answer 1

Answer: (D)

$5\times {10}^{-7}nm$

Resistance of the wire $R=\frac{V}{I}$

$\therefore$ $R=\frac{2}{4}=0.5$ A

Cross-section area of wire $A=1m{m}^2={10}^{-6}{m}^2$

Length of wire $L=1m$

Thus resistivity of wire $\rho =\frac{RA}{L}$

$\therefore$ $\rho =\frac{0.5\times {10}^{-6}}{1}=5\times {10}^{-7}\Omega m$