Question

We are given a piece of copper of mass m=0.82 g to form a cylindrical wire of resistance R=0.87.2. What should be the length / of this wire?: 2.16 m. What would be the diameter d of this wire?: d 0.232 mm. To make things certain, let us use copper's mass density of 8.96 g/cm3 and resistivity p= 1.7 x 10-8 2.m.

Answer 1

Length of wire=2.16 m

Diameter of wire=0.232 mm

Step-by-step explanation:

m= mass of copper wire= 0.82 g

R= Resistance of copper wire= 0.87 ohms

D= Density of copper= 8.96 g/cm^3

ρ= Resistivity= 1.7×10^-8 Ωm

`Density=(mass)/(volume)\\\Rightarrow volume=(mass)/(density)\\\Rightarrow volume=\frac {0.82}{8.96}\\\Rightarrow volume=0.091\ cm^3\\ volume = \pi r^2 l\\\Rightarrow \pi r^2=(volume)/(l)\\ \Rightarrow \pi r^2=\frac {0.091}{l}\\`

`\rho=R(A)/(l)\\\Rightarrow 1.7* 10^(-8)=0.87 (\pi r^2)/(l)\\\Rightarrow 1.7* 10^(-8)=0.87 (0.091* 10^(-6))/(l^2)\\\Rightarrow l^2=\frac {0.87* 0.091* 10^(-6)}{1.7* 10^(-8)}\\\Rightarrow l^2=0.046* 10^2\\\Rightarrow length=2.16\ m`

`\pi r^2=\frac {0.091}{l}\\\Rightarrow r^2=\frac {0.091* 10^(-6)}{2.16 \pi}\\\Rightarrow r^2=1.34* 10^(-8)\\\Rightarrow r=0.00011\ m\\\Rightarrow d=0.000232\ m\\\therefore diameter=0.232\ mm`