A nichrome wire 1 m long and of cross-sectional area \( 1\,\mathrm{mm^2} \) draws a current of 4 A at 2 V. The resistivity of nichrome is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 5\times10^{-7}\,\Omega\,\mathrm{m} \)
Ohm’s law gives the resistance of the wire from the voltage and the current, \( R=V/I \). The resistance depends on the length and cross-section as \( R=\rho l/A \), so the resistivity is \( \rho=RA/l \).
\( \begin{aligned} R &= \frac{V}{I} \\ &= \frac{2\,\mathrm{V}}{4\,\mathrm{A}} \\ &= 0.5\,\Omega \end{aligned} \)
\( A=1\,\mathrm{mm^2}=1\times10^{-6}\,\mathrm{m^2} \)
\( l=1\,\mathrm{m} \)
\( \begin{aligned} \rho &= \frac{RA}{l} \\ &= \frac{0.5\,\Omega\times1\times10^{-6}\,\mathrm{m^2}}{1\,\mathrm{m}} \\ &= 5\times10^{-7}\,\Omega\,\mathrm{m} \end{aligned} \)