What is the resistance of a 7.4-m length of copper wire 1.2mm in diameter? The resistivity of copper is 1.68×10−8Ω⋅m.
R=_________
To find the resistance of a copper wire, we can use the formula:
R = (ρ * L) / A
Where:
R is the resistance,
ρ (rho) is the resistivity of copper,
L is the length of the wire,
A is the cross-sectional area of the wire.
In this case, we are given:
ρ = 1.68×10−8Ω⋅m
L = 7.4 m
diameter = 1.2mm
First, let's calculate the cross-sectional area of the wire.
The diameter is given as 1.2mm, but we need the radius. Therefore, we divide the diameter by 2:
radius = diameter / 2 = 1.2mm / 2 = 0.6mm
Now, let's convert the radius to meters:
radius = 0.6mm / 1000 = 0.0006m
Next, let's calculate the cross-sectional area:
A = π * r^2
= π * (0.0006m)^2
= 0.000001131 m²
Now, substitute the values into the formula:
R = (ρ * L) / A
= (1.68×10−8Ω⋅m * 7.4m) / 0.000001131 m²
= 1.24 Ω
Therefore, the resistance of a 7.4-m length of copper wire with a diameter of 1.2mm is 1.24 Ω.