Question

A wire 50 cm long and $1m{m}^2$ 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

The correct option is D $1\times {10}^{-6}\Omega m$

By Ohm's law, resistance can be found from current and voltage as below.

$R=\frac{V}{I}$
$=\frac{2}{4}=\frac{1}{2}\Omega$

The resistance R is dependent on resistivity, length and area of cross-section as below,

$R=\rho \frac{l}{A}$
$\Rightarrow \frac{1}{2}=\frac{\rho \times 0.50m}{{10}^{-6}{m}^2}$

This implies the resistivity of the wire is:
$\Rightarrow {10}^{-6}\Omega m$