The resistance of eureka wire is `2.5 Omega`. What is the value of specific resistance of write of 14 m length and diameter of 0.14 cm ?

Options

A. `27.5xx10^(-6)Omega - cm`
B. `20.6xx10^(-6)Omega - cm`
C. `25.3xx10^(-6)Omega - cm`
D. None of the above

Answer

A

Explanation

Length of wire, `l=14 mxx100=1400 cm`
Diameter of wire = 0.14 cm
`therefore " "` Radius of wire `r=(0.14)/(2)=0.07 cm`
Cross-sectionl area of wire `= pi r^(2)=pi(0.07)^(2)`
Resistance of wire `= 2.5 Omega`
By formula, `R = rho (l)/(A)`
`rArr " " rho=(AR)/(l)=(pixx(0.07)^(2)xx2.5)/(1400)`
`" " = (pixx0.07xx0.07xx2.5)/(1400)`
or `" " rho = 27.5xx10^(-6)Omega - cm`