Respuesta :
Answer:
Resistance = 1.2704 Ω
Step-by-step explanation:
Resistance of a conductor (R) is directly proportional to the length of the conductor (L)
⇒ R ∝ L
⇒ R = k·L , where k is called proportionality constant
Now, it is given for 250 foot wire , R = 0.397 Ω
⇒ 0.397 = k·250
⇒ k = 0.001588
So, Resistance for 800 foot of same conductor :
Resistance = 0.001588 × 800
⇒ Resistance = 1.2704 Ω
The resistance of the cooper conductor at 800 feet is [tex]\boxed{1.27{\text{ }}\Omega }.[/tex]
Further explanation:
The proportionality equation can be expressed as follows,
[tex]y \propto x[/tex]
The value of [tex]y[/tex] changes as [tex]x[/tex] changes. If the value of [tex]x[/tex] increases then the value of [tex]y[/tex] is also increasing.
The inversely proportional relationship can be expressed as,
[tex]y \propto \dfrac{1}{x}[/tex]
The equation can be expressed as follows,
[tex]y = kx[/tex]
Here, k is the proportionality constant.
Given:
The resistance of the copper conductor is [tex]0.397{\text{ }}\Omega[/tex] if the length is [tex]\boxed{250{\text{ foot}}}.[/tex]
Explanation:
The relationship between the resistance and the length of the conductor can be expressed as follows,
[tex]\boxed{R = \frac{{\rho \times L}}{A}}[/tex]
The resistance of the conductor is directly proportional to the length of the conductor.
If the length of the wire increases then the resistance will also increases.
The resistance at 250 feet is 0.397 ohm.
[tex]0.397 = \dfrac{\rho }{A} \times 250[/tex]
The resistance of the cooper conductor at 800 feet can be obtained as follows,
[tex]\begin{aligned}\frac{R}{{0.397}}&=\frac{{\dfrac{\rho }{A} \times 800}}{{\dfrac{\rho }{A} \times 250}}\\\frac{R}{{0.397}}&=\frac{{800}}{{250}}\\\frac{R}{{0.397}} &= 3.2\\R &= 3.2 \times 0.397\\R &= 1.27\\\end{aligned}[/tex]
The resistance of the cooper conductor at 800 feet is [tex]\boxed{1.27{\text{ }}\Omega }.[/tex]
Learn more:
- Learn more about inverse of the function https://brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
- Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Ratio and proportion
Keywords: proportional, 250-foot, copper conductor, resistance, 0.397, same conductor, 800 feet, directly proportional, constant, proportionality equation, constant of proportionality.
