Question

A rod of a certain metal is $1.0 m$ long and $0.6 cm$ in diameter. Its resistance is $3.0 \times 10^{-3}$ ohm. 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. $1.35 \times 10^{-8} ohm$
• 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
$\rho=\frac{R A}{l}=\frac{3 \times 10^{-3} \pi\left(0.3 \times 10^{-2}\right)^{2}}{1}$
$=27 \times 10^{-9} \pi \Omega m$
Resistance of $\operatorname{disc} R=\rho \frac{\text { Thickness }}{\text { Area of cross section }}$
$=27 \times 10^{-9} \pi \times \frac{\left(10^{-3}\right)}{\pi \times\left(1 \times 10^{-2}\right)^{2}}$
$=2.7 \times 10^{-7} \Omega$