Question

A copper rod of length $20\text{cm}$ and cross-sectional area $2{\text{mm}}^2$ is joined with a similar aluminium rod as shown below. Find the resistance of the combination between the ends. Resistivity of copper $=1.7\times {10}^{-8}\Omega \text{m}$ and that of aluminium $=2.6\times {10}^{-8}\Omega \text{m}$ .

• A. $4\text{m}\Omega$
• B. $3\text{m}\Omega$
• C. $2\text{m}\Omega$
• D. $1\text{m}\Omega$

Answer 1

The correct option is D $1\text{m}\Omega$

Resistance of copper rod is $=\frac{{\rho }_{\text{cu}}l}{A}$
$=\frac{1.7\times {10}^{-8}\times 0.2}{2\times {10}^{-6}}=0.0017\Omega$

Resistance of aluminium rod is $=\frac{{\rho }_{\text{al}}l}{A}$
$=\frac{2.6\times {10}^{-8}\times 0.2}{2\times {10}^{-6}}=0.0026\Omega$

These resistances are in parallel and thus their equivalent resistance is

$\frac{1}{R_{\text{eq}}}=\frac{1}{R_{\text{cu}}}+\frac{1}{R_{\text{al}}}$

$\therefore R_{\text{eq}}=0.001\Omega$