100 mg mass of nichrome metal is drawn into a wire of area of cross-section 0.05 mm. Calculate the resistance of this wire. Given density of nichrome` 8.4 xx 10^3 "kgm"^(-3)` and resistivity of the material as `1.2 xx 10^(-6) Omega` m.

Explanation

Given mass = 100 mg =`10^2xx10^(-6)=10^(-4)` kg
area of cross section A = `5xx10^(-2) xx (10^(-3))^2m^2`
i.e., `A=5xx10^(-8)m^2` . Density `D=8.4xx10^3 kgm^(-3), rho=1.2xx10^(-6) Omegam` but
density = `"mass"/"volume"`
i.e. volume = `"mass"/"density"=10^(-4)/(8.4xx10^3)`
`=(0.119xx10^(-7))/(5xx10^*(-8))=0.0238xx10`
i.e. length = 0.238 m
We know that , `R=(rhol)/A =(1.2xx10^(-6)xx0.238)/(5xx10^(-8))`
=0.05712 x 100
or R=5.712 `Omega`
Resistance of the wire = `5.712Omega`.