Question

A nichrome wire $50\, cm$ long and $1\, mm ^{2}$ in cross-section carries a current of $4\, A$ when connected to a $2\, V$ storage battery. The resistivity of nichrome is

• A. $1 \times 10^{-6} \Omega \,m$
• B. $2 \times 10^{-7} \Omega \,m$
• C. $4 \times 10^{-7} \Omega\, m$
• D. $5 \times 10^{-7} \Omega \,m$

Answer 1

Answer: (A)

Here, $l=50\, cm =50 \times 10^{-2}\, m$
$A=1 mm ^{2}=1 \times 10^{-6} m ^{2}, V=2\, V,\, I=4 A$
According to Ohm's law, $V=I R$
or $R=\frac{V}{I}=\frac{2}{4}=\frac{1}{2} \Omega$...(i)
Resistance of a wire is $R=\rho \frac{l}{A}$
or $\rho \frac{l}{A}=\frac{1}{2}$ (Using (i))
$\therefore \rho=\frac{A}{2 l}=\frac{10^{-6}}{2 \times 50 \times 10^{-2}}=10^{-6} \Omega\, m$