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

`l_(1) = 1m, r_(1) = 0.3 cm = 0.3 xx 10^(-2) m, R_(1) = 3 xx 10^(-3)Omega, I_(2) = 1 xx 10^(-3) Omega, I_(2) = 1 xx 10^(-3), r_(2) = 1 xx 10^(-2) m`,
`R_(1) = (rho l_(1))/A_(1) rArr rho =(R_(1)A_(1))/I_(1) = (3 xx 10^(-3) xx pi xx (0.3 xx 10^(-2))^(2))/1`
`= 27 xx 10^(-9) pi Omega`m
For 2nd disc.
`R_(2) = rhol_(2)/A_(2) = (27 xx 10^(-9) xx pi xx 10^(-3))/(pi xx (1 xx 10^(-2)))^(2) = 2.7 xx 10^(-7)Omega`