Question

A rod of a certain metal is 1.0 m long and 0.6 cm in diameter. Its resistance is $3.0\times {10}^{-3}\Omega$. Another disc made of the same metal is 2.0 cm in diameter and 1.0 mm thick. What is the resistance between the round faces of the disc?

• A. $1.35\times {10}^{-8}\Omega$
• B. $2.70\times {10}^{-7}\Omega$
• C. $4.05\times {10}^{-6}\Omega$
• D. $8.10\times {10}^{-5}\Omega$

Answer 1

The correct option is B $2.70\times {10}^{-7}\Omega$

Resistivity of the material of the rod
$\rho =\frac{RA}{l}=\frac{3\times {10}^{-3}\times {\pi (0.3\times {10}^{-2})}^2}{1}$
$=27\times {10}^{-9}\pi \Omega$
Resistance of disc,
$R=\frac{Resistivityofrod\times thickness}{Areaofcross-section}$
$=27\times {10}^{-9}\pi \times \frac{{10}^{-3}}{\pi \times {(1\times {10}^{-2})}^2}$
$=27\times {10}^{-7}\Omega$