Q. A resistor is constructed as hollow cylinder of dimensions $r_{a} = 0.5\ cm$ and $r_{b} = 1.0cm$ and $\rho = 3.5 \times 10^{- 5}\Omega m$. The resistance of the configuration for the length of 5 cm cylinder is $\ldots. \times 10^{- 3}\Omega.$
A) 7.42
B) 10.56
C) 14.38
D) 16.48
Explanation
(a) Given,
$l = 5cm = 5 \times 10^{- 2}m,\ $
$\rho = 3.5 \times 10^{- 5}\Omega m$
$A = \pi\left( 1 \times 10^{- 4} - 0.25 \times 10^{- 4} \right)$
$= 0.75\pi \times 10^{- 4}m$
$= 7.5\pi \times 10^{- 5}m$
$\therefore\ \ \ R = \frac{\rho l}{A} = \frac{3.5 \times 10^{- 5} \times 5 \times 10^{- 2}}{7.5\pi \times 10^{- 5}}$
$= 7.42 \times 10^{- 3}\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.