Given:
Length of wire = 1 km
Diameter of wire = 1 mm
Rsistivity of constantan = 4.9x10⁻⁷ Ωm
Resistivity of copper = 1.7 x 10⁻⁸ Ωm
Let's calculate the resistance of each material.
To find the resistance, apply the formula:
[tex]R=\frac{p\ast l}{A}[/tex]
Where:
R is the resistance
p is the resistivity
l is the length of wire
A is the cross-sectional Area.
(a) Constantan:
Where:
p = 4.9x10⁻⁷ Ωm
l = 1 km = 1000 m
To find the cross sectional area, we have:
[tex]A=\frac{\pi d^2}{4}=\frac{\pi\ast(1\ast10^{-3})}{4}=7.85\ast10^{-7}m^2[/tex]
Thus, we have:
[tex]\begin{gathered} R=\frac{p\ast l}{A} \\ \\ R=\frac{4.9\ast10^{-7}\ast1000}{7.85\ast10^{-7}} \\ \\ R=623.88\Omega\approx620\Omega \end{gathered}[/tex]
Therefore, the resistance of constantan is 620 Ω.
(b) Resistance of copper:
Where:
p = 1.7 x 10⁻⁸ Ωm
l = 1 km = 1000 m
A = 7.85 x 10⁻⁷m²
Thus, we have:
[tex]\begin{gathered} R=\frac{p\ast l}{A} \\ \\ R=\frac{1.7\ast10^{-8}\ast1000}{7.85\ast10^{-7}} \\ \\ R=21.6\text{ }\Omega\approx22\Omega \end{gathered}[/tex]
Therefore, the resistance of the copper is 22 Ω.
(c) We can see the resistance of the copper is less than the resistance of constantan.
Therefore, this means the constantan has a higher resistance than copper..
Therefore, the best material that is suited to make resistors will be the constantan .
ANSWERS:
(a) 620 Ω
(b) 22 Ω
(c) Constantan
