Respuesta :
Explanation:
Given that,
Mass of Nichrome, m = 0.5 g
The resistance of the wire, R = 0.673 ohms
Resistivity of the nichrome wire, [tex]\rho=10^{-6}\ \Omega -m[/tex]
Density, [tex]d=8.31\times 10^3\ kg/m^3[/tex]
(A) The length of the wire is given by using the definition of resistance as :
Volume,
[tex]V=A\times l\\\\A=\dfrac{V}{l}\\\\Since, V=\dfrac{m}{d}\\\\V=\dfrac{m}{d}\\\\V=\dfrac{0.5\times 10^{-3}}{8.31\times 10^3}\\\\V=6.01\times 10^{-8}\ m^3[/tex]
Area,
[tex]A=\dfrac{V}{l}\\\\A=\dfrac{6.01\times 10^{-8}}{l}[/tex]....(1)
[tex]R=\rho \dfrac{l}{A}\\\\l=\dfrac{RA}{\rho}\\\\l=\dfrac{0.673\times 6.01\times 10^{-8}}{l\times 10^{-6}}\\\\l=0.201\ m[/tex]
(b) Equation (1) becomes :
[tex]A=\dfrac{6.01\times 10^{-8}}{l}\\\\A=\dfrac{6.01\times 10^{-8}}{0.201}\\\\\pi r^2=3\times 10^{-7}\\\\r=\sqrt{\dfrac{3\times 10^{-7}}{\pi}} \\\\r=3.09\times 10^{-4}\ m[/tex]
Hence, this is the required solution.
