Respuesta :
Answer with Explanation:
We are given that
Length of wire 1=[tex]L_1[/tex]
Length of wire 2=[tex]L_2[/tex]
Resistivity of copper wire=[tex]\rho_1=1.7\times 10^{-5}\Omega-m[/tex]
Resistivity of aluminum wire=[tex]\rho_2=2.82\times 10^{-5}\Omega-m[/tex]
Wire 1=Copper wire
Wire 2=Aluminum wire
Diameter of both wires are same and resistance of both wires are also same.
We know that
Resistance =[tex]\frac{\rho l}{A}[/tex]
When diameter of wires are same then their cross section area are also same .
[tex]l=\frac{RA}{\rho}[/tex]
When resistance and area are same then the length of wire depend upon the resistivity of wire .
The length of wire is inversely proportional to resistivity.
When resistivity is greater then the length of wire will be short and when the resistivity is small then the length of wire will be large.
[tex]\rho_1<\rho_2[/tex]
Therefore, [tex]L_1>L_2[/tex]
Hence, the length of wire 1 (copper wire) is greater than the length of wire 2 (aluminum).
[tex]\frac{L_1}{L_2}=\frac{\frac{RA}{1.7\times 10^{-5}}}{\frac{RA}{2.82\times 10^{-5}}}=1.66[/tex]
[tex]L_1=1.66L_2[/tex]
The comparison between [tex]L_{1} and L_{2}[/tex] is that [tex]L_{1}[/tex] is greater.
What is Resistance?
Given that,
[tex]L_{1}[/tex] as the height of the first wire
[tex]L_{2}[/tex] as the height of the second wire
Resistance of the wire made of copper = 1.7 × 10 –5 Ω·m
Resistance of the wire made of aluminum = 2.82 × 10 –5 Ω·m
As we know,
Resistance [tex]= V / I[/tex]
Since the diameter of the wires remains equal, the resistance would remain the same as well.
Because the resistivity of a metal is inversely proportional to the length it possesses, this implies that the shorter the length, the greater the resistivity.
Thus,
[tex]L_{1}[/tex] would be longer as its resistivity is lesser than [tex]p_{2}[/tex]
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