A copper rod of length 20 cm and cross-sectional area 2 ~mm^2 is...

A copper rod of length 20 cm and cross-sectional area

2 \mathrm{~mm}^2

is joined with a similar aluminium rod as shown below 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

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

The resistance of pair of rods is

\left(\rho_{\mathrm{Al}}=2.6 \times 10^{-8} \quad \Omega-\mathrm{m}\right. and \quad \rho_{\mathrm{Cu}}=1.7 \times 10^{-8} \Omega-\mathrm{m})

Options

A $1.0 \mathrm{~m} \Omega$
B $2.0 \mathrm{~m} \Omega$
C $3.0 \mathrm{~m} \Omega$
DNone of these

Correct answer

A. $1.0 \mathrm{~m} \Omega$

Step-by-step solution

The resistance of the copper rod

=\rho \frac{1}{a}

=\frac{1.7 \times 10^{-8} \times 20 \times 10^{-2}}{2.0 \times 10^{-6}}=1.7 \times 10^{-3} \Omega

Similarly the resistance of aluminium rod

=2.6 \times 10^{-3} \Omega

The equivalent resistance

\begin{aligned} & \frac{1}{R}=\frac{1}{1.7 \times 10^{-3}}+\frac{1}{2.6 \times 10^{-3}} \\ & R=\frac{1.7 \times 2.6}{4.3} \times 10^{-3}=1.0 \mathrm{~m} \Omega\end{aligned}

Practice Current Electricity on Quantrex Academy →

More from Current Electricity