A rod of certain metal is `1.0 m` long and `0.6 cm` in diameter. Its resistance is `3.0 xx 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?

Options

A. `1.35 xx 10^(-8) ohm`
B. `2.70 xx 10^(-7) ohm`
C. `4.05 xx 10^(-6) ohm`
D. `8.10 xx 10^(-5) ohm`

Answer

B

Explanation

(b) Resistivity of the material of the rod
`rho = (RA)/(1) = (3 xx 10^(-3) pi (0.3 xx 10^(-2))^(2))/(1) = 27 xx 10^(-9) pi Omega xx m`
Resistance of disc `R = (("Thickness"))/(("Area of cross section"))`
`= 27 xx 10^(-9) pi xx ((10^(-3)))/(pi xx (1 xx 10^(-2))^(2)) = 2.7 xx 10^(-7) Omega`.