Question

Find the resistance of a hollow cylindrical pipe of length 1 m whose inner and outer radii are 10 cm and 20 cm respectively. Assume that the cylindrical pipe is made of a material of resistivity $2\times {10}^{-8}\Omega m$.

• A. $0.21m\Omega$
• B. $0.21\Omega$
• C. $0.21\mu \Omega$
• D. $21\Omega$

Answer 1

The correct option is C

$0.21\mu \Omega$

Given:
Resistivity $\rho =2\times {10}^{-8}\Omega m$
Length of cylinder, $L=1m$
Inner radius $R_i=10cm=0.1m$
Outer radius $R_o=20cm=0.2m$

Area of cylinder material,
$A=\pi (R_o^2-R_i^2)$
$A=\pi ({0.2}^2-{0.1}^2)m^2$
$A=0.0942m^2$

Resistance is given by:
$R=\rho \frac{L}{A}$
$R=2\times {10}^{-8}\times \frac{1}{0.0942}$
$R=0.21\times {10}^{-6}\Omega$
$R=0.21\mu \Omega$