Respuesta :
Answer with Explanation:
Let r be the resistance of short piece of copper wire.
Resistance of copper wire=R=[tex]13\Omega[/tex]
Resistance is directly proportional to length.
If a wire has greater resistance then,the wire will be greater in length.
Therefore,resistance of long piece of wire=7r
Total resistance of copper wire=Sum of resistance of two piece of wires
[tex]r+7r=13[/tex]
[tex]8r=13[/tex]
[tex]r=\frac{13}{8}[/tex]ohm
Resistance of long piece of wire=[tex]7\times\frac{13}{8}=\frac{91}{8}\Omega[/tex]
Resistance of short piece of wire =[tex]\frac{13}{8}\Omega[/tex]
Resistivity of wire and cross section area of wire remains same .
Let L be the total length of wire and L' be the length of short piece of wire.
We know that
[tex]R=\frac{\rho L}{A}[/tex]=[tex]\frac{\rho}{A}L=KL[/tex]
[tex]\frac{R}{L}=K[/tex]
Where K=[tex]\frac{\rho}{A}[/tex]=Constant
Using the formula
[tex]\frac{13}{L}=\frac{\frac{13}{8}}{L'}[/tex]
[tex]\frac{L'}{L}=\frac{13}{8}\times \frac{1}{13}=\frac{1}{8}[/tex]
[tex]L'=\frac{L}{8}[/tex]
Length of short piece of wire=L'=[tex]\frac{L}{8}[/tex]
Length of long piece of wire=[tex]L-L'=L-\frac{L}{8}=\frac{8L-L}{8}=\frac{7}{8}L[/tex]
% of length of short piece of wire=[tex]\frac{\frac{L}{8}}{L}\times 100=12.5%[/tex]%
The resistance of the short piece=[tex]\frac{13}{8}\Omega[/tex]
The resistance of the long piece=[tex]\frac{91}{8}\Omega[/tex]
The length of short piece wire is [tex]12.5[/tex] % of total wire length.
The resistance of the short piece wire is [tex]\frac{13}{8}ohms[/tex]
The resistance of the long piece wire is, [tex]7*\frac{13}{8}=\frac{91}{8}ohms[/tex]
Resistance :
Let us consider that resistance of short piece wire is r.
So that, resistance of long piece wire is [tex]7r[/tex].
Total resistance of wire is [tex]13[/tex] ohms.
[tex]7r+r=13\\\\8r=13\\\\r=\frac{13}{8}Ohm[/tex]
- The resistance of the short piece wire is [tex]\frac{13}{8}ohms[/tex]
- The resistance of the long piece wire is, [tex]7*\frac{13}{8}=\frac{91}{8}ohms[/tex]
- The resistance of wire is directly proportional to length of wire.
Let us consider that total length of wire is 13L.
So that, length of short piece wire [tex]=\frac{13}{8} L[/tex]
length of short piece wire is,
[tex]=\frac{\frac{13}{8}L }{13L}*100 =\frac{1}{8} *100=12.5[/tex]
The length of short piece wire is 12.5 % of total wire length.
Find out more information about the Resistance here:
https://brainly.com/question/17563681
