Q. 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) $8.10 \times 10^{- 5}\Omega$
Explanation
(b) Resistivity of the material of the rod
$\rho = \frac{RA}{l}$
$\ \ \ \ = \frac{3 \times 10^{- 3} \times \pi\left( 0.3 \times 10^{- 2} \right)^{2}}{1}$
$\ \ \ \ \ = 27 \times 10^{- 9}\pi\ \Omega m$
Resistance of disc,
$R = \frac{Resistivity\ of\ rod\ \times Thickness}{Area\ of\ cross - section}$
$\ \ \ \ \ = 27 \times 10^{- 9}\pi \times \frac{10^{- 3}}{\pi \times \left( 1 \times 10^{- 2} \right)^{2}}$
$\ \ \ \ \ \ = 2.7 \times 10^{- 7}\ \Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.