Question
What is the resistance of a 100m length of copper wire with a diameter of 2mm at 20°C?
Answers
Answered by
GPT 3.5
The resistance of a wire can be calculated using the formula:
R = (ρ * L) / A
where R is the resistance, ρ (rho) is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
The resistivity of copper at 20°C is approximately 1.72 x 10^-8 Ωm.
The length of the wire is given as 100m.
To calculate the cross-sectional area, we need the radius of the wire, which is half of the diameter. So, the radius is 2mm / 2 = 1mm = 0.001m.
The cross-sectional area can be calculated using the formula:
A = π * r^2
where r is the radius.
Therefore, the cross-sectional area is:
A = π * (0.001m)^2 = 3.14159 * 0.000001m^2 = 3.14159 x 10^-6 m^2.
Now we can use the values in the resistance formula:
R = (1.72 x 10^-8 Ωm * 100m) / (3.14159 x 10^-6 m^2)
R = 1.72 x 10^-6 Ω / 3.14159 x 10^-6 m^2
R ≈ 0.547 Ω
Therefore, the resistance of a 100m copper wire with a diameter of 2mm at 20°C is approximately 0.547 Ω.
R = (ρ * L) / A
where R is the resistance, ρ (rho) is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
The resistivity of copper at 20°C is approximately 1.72 x 10^-8 Ωm.
The length of the wire is given as 100m.
To calculate the cross-sectional area, we need the radius of the wire, which is half of the diameter. So, the radius is 2mm / 2 = 1mm = 0.001m.
The cross-sectional area can be calculated using the formula:
A = π * r^2
where r is the radius.
Therefore, the cross-sectional area is:
A = π * (0.001m)^2 = 3.14159 * 0.000001m^2 = 3.14159 x 10^-6 m^2.
Now we can use the values in the resistance formula:
R = (1.72 x 10^-8 Ωm * 100m) / (3.14159 x 10^-6 m^2)
R = 1.72 x 10^-6 Ω / 3.14159 x 10^-6 m^2
R ≈ 0.547 Ω
Therefore, the resistance of a 100m copper wire with a diameter of 2mm at 20°C is approximately 0.547 Ω.
There are no human answers yet. A form for humans to post answers is coming very soon!