Question

A copper rod of length 20 cm and cross-sectional area 2 mm${}^2$ is joined with a similar aluminium rod as shown below
The resistance of pair of rods is (${\rho }_{Al}=2.6\times {10}^{-8}\Omega -m$ and ${\rho }_{Cu}=1.7\times {10}^{-8}\Omega -m$)

• A. 1.0 m $\Omega$
• B. 2.0 m $\Omega$
• C. 3.0 m $\Omega$
• D. None of these

Answer 1

The correct option is A 1.0 m $\Omega$

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

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

These resistances are in parallel and thus their equvalent resistance is $1m\Omega$.