Question

A rod made up of metal is $1.2m$ long and $0.8cm$ in diameter. Its resistance is $3.5\times {10}^{-3}\Omega$. Another disc made up of the same metal is $2.0cm$ in diameter and $1.25mm$ 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. $5.82\times {10}^{-7}\Omega$
• D. $8.10\times {10}^{-6}\Omega$

Answer 1

Answer: (C)

$5.82\times {10}^{-7}\Omega$

Given, $l=1.2m$, $d=0.8cm⟹=r=0.4cm$
$R=3.5\times {10}^{-3}\Omega$, thickness $=1.25mm$.
Resistivity of the material of the rod
$\rho =\frac{RA}{l}=\frac{3.5\times {10}^{-3}\times \pi {(0.4\times {10}^{-2})}^2}{1.2}$
$=46.6\times {10}^{-9}\pi \Omega m$
Resistance of disc, $R=\frac{\rho \left(Thickness\right)}{Areaofcross-section}$
$=\frac{46.6\times {10}^{-9}\pi \times (1.25\times {10}^{-3})}{\pi {(1\times {10}^{-2})}^2}$
$=5.82\times {10}^{-7}\Omega$