Question

A resistor is constructed as a hollow cylinder with inner and outer radii $r_{a}=0.5 \, cm$ , $r_{b}=1.0 \, cm$ respectively and resistivity $\rho =3.5\times 10^{- 5} \, \Omega \, m$ . The resistance of the configuration for the length of $5 \, cm$ cylinder is $\times 10^{- 3} \, \Omega $ .

• A. $\text{7.42}$
• B. $\text{10.56}$
• C. $\text{14.38}$
• D. $\text{16.48}$

Answer 1

Answer: (A)

Given.
$l=5 cm =5 \times 10^{-2} m$
$\rho=3.5 \times 10^{-5} \Omega m$
$A=\pi\left(1 \times 10^{-4}-0.25 \times 10^{-4}\right)$
$=0.75 \pi \times 10^{-4} m ^{2}$
$=7.5 \pi \times 10^{-5} m ^{2}$
$\therefore R=\frac{\rho l}{A}=\frac{3.5 \times 10^{-5} \times 5 \times 10^{-2}}{7.5 \pi \times 10^{-5}}$
$=7.42 \times 10^{-3} \Omega$