Question

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

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

Answer 1

Answer: (D)

Length $(l)=50\, cm =0.5\, m$;
Area $(A)=1\, mm ^{2}=1 \times 10^{-6}\, m ^{2}$;
Current $(I)=4 A$ and voltage $(V)=2$ volts.
Resistance $(R)=\frac{V}{I}=\frac{2}{4}=0.5\, \Omega$ and
Resistivity $(\rho) =R \times \frac{A}{l}=0.5 \times \frac{1 \times 10^{-6}}{0.5}$
$=1 \times 10^{-6}\, \Omega . m .$