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Riplilpeep
18.03.2021 •
Physics
What is the electric resistance of a copper wire 0.65 m long with a diameter of 2 mm?
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Ответ:
To calculate resistance, we will use the formula:
R = ρl / A
where ρ(rho) is the resistivity of the material, l is the length of the wire and A is the cross-sectional area
We are given:
Length of wire (l) = 0.65 m
Diameter of wire (d) = 2 mm
Material of wire: Copper
Some important conversions:
- radius of the wire = diameter/2
radius = 2 mm/2 = 1 mm OR 1 * 10⁻³m
Calculating the cross-sectional area:
Cross-sectional area is the area of the circle at the end of the wire.
Cross-sectional area = π(r²)
Area = π(1 * 10⁻³)² [replacing the value of r]
Area = π * 10⁻⁶ m²
Calculating the resistance:
using the formula mentioned before:
R = ρl / A
R =
[resistivity of copper = 1.7 × 10⁻⁸ Ωm]
R = 3.52 * 10⁻³ (approx)
Ответ:
3.5 × 10⁻³ Ω
Explanation:
The resistance of a conductor is calculated by the formula:
Let's start by converting the diameter of the copper wire to meters.
2 mm → .002 mSince we want the radius of the cross-section, we will divide .002 m by 2.
.002/2 = .001 mThe radius of the copper wire is .001 m. We can calculate the area of the circular cross-section by using the formula:
The area of the cross-section is π · 10⁻⁶ m².
The length of the wire is 0.65 m long. We do not have to convert units for the length of the wire since it is already in the SI units: meters.
Assuming the copper wire is at 20°C, we know that its resistivity is 1.7 · 10⁻⁸ Ω · m.
Using these three variables, we can solve for R in the formula for electric resistance.
ρ = 1.7 · 10⁻⁸ Ω · m l = 0.65 m A = π · 10⁻⁶ m²Substitute these values into the equation.
Notice how the unit m² cancels out, leaving us with Ω (units of electrical resistance).
The electric resistance of a copper wire 0.65 m long with a radius of .001 m is .0035 ohms (Ω), or 3.5 × 10⁻³ Ω.
Ответ:
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