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A nichrome wire 50 cm long and of cross-sectional area $1\,\text{mm}^2$ carries a current of 4 A when connected to a 2 V battery. The resistivity of the nichrome wire in $\Omega\,\text{m}$ is:

1. $1 \times 10^{-6}$
2. $4 \times 10^{-7}$
3. $3 \times 10^{-7}$
4. $2 \times 10^{-7}$

Correct answer: $1 \times 10^{-6}$

Solution

From Ohm’s law, $R=V/I=2/4=0.5\,\Omega$. Using $\rho=RA/L$ with $L=0.5\,\text{m}$ and $A=1\,\text{mm}^2=10^{-6}\,\text{m}^2$, we get $\rho=10^{-6}\,\Omega\,\text{m}$.

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