Respuesta :
Answer:
The potential difference across iron wire is 133.95 V
Solution:
As per the question:
Length, l = 2.97 m
Diameter. d = 0.88 mm = [tex]0.88\times 10^{- 3}\ m[/tex]
Voltage, V = 157 V
Now,
We know that the resistivity of iron, [tex]\rho_{I} = 10\ S[/tex]
Resistivity of copper, [tex]\rho_{I} = 1.72\ S[/tex]
Now,
The potential difference across the iron wire:
V' = [tex]\frac{\rho_{I}V}{\rho_{I} + \rho_{C}}[/tex]
V' = [tex]\frac{10\times 157}{10 + 1.72} = 133.95\ V[/tex]
Answer:
The potential difference across the iron wire 134.2 V.
Explanation:
Given that,
Length = 2.97 m
Diameter = 0.88 mm
Total potential = 157 V
We know that,
The resistivity of iron wire
[tex]\rho_{i}=10\times10^{-8}\Omega m[/tex]
The resistivity of copper wire
[tex]\rho_{c}=1.7\times10^{-8}\Omega m[/tex]
The voltage for each wire is proportional to the resistivity.
We need to calculate the resistance for copper wire
Using formula of resistance
[tex]R_{c}=\dfrac{\rho\times l}{A}[/tex]
Put the value into the formula
[tex]R_{c}=\dfrac{1.7\times10^{-8}\times2.97}{\pi\times(0.44\times10^{-3})^2}[/tex]
[tex]R_{c}=0.0830\ \Omega[/tex]
We need to calculate the resistance for iron wire
Using formula of resistance
[tex]R_{i}=\dfrac{\rho\times l}{A}[/tex]
Put the value into the formula
[tex]R_{i}=\dfrac{10\times10^{-8}\times2.97}{\pi\times(0.44\times10^{-3})^2}[/tex]
[tex]R_{i}=0.4883\ \Omega[/tex]
The total resistance is
[tex]R =R_{c}+R_{i}[/tex]
[tex]R=0.0830+0.4883[/tex]
[tex]R=0.5713\ \Omega[/tex]
We need to calculate the potential difference across the iron wire
Using formula of potential difference
[tex]V_{i}=\dfrac{VR_{i}}{R}[/tex]
Put the value into the formula
[tex]V_{i}=\dfrac{157\times0.4883}{0.5713}[/tex]
[tex]V_{i}=134.2\ V[/tex]
Hence, The potential difference across the iron wire 134.2 V.
