Question

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

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

Answer 1

Answer: (B)

Resistivity of the material of the rod
$\rho =\frac{RA}{l}=\frac{3\times 10^{-3}\pi {\left(0.3\times 10^{-2}\right)}^2}{1}$
$=27\times 10^{-9}\pi \Omega m$
Resistance of $\mathrm{disc}R=\rho \frac{\text{ Thickness }}{\text{ Area of cross section }}$
$=27\times 10^{-9}\pi \times \frac{\left(10^{-3}\right)}{\pi \times {\left(1\times 10^{-2}\right)}^2}$
$=2.7\times 10^{-7}\Omega$