A copper wire has a resistivity of 1.723 x 10-8 Ω-m and a cross-sectional area of 9.5 mm2. Calculate the length of the wire in m when its resistance is 3.2 Ω.
Question
A copper wire has a resistivity of 1.723 x 10^-8 Ω-m and a cross-sectional area of 9.5 mm². Calculate the length of the wire in m when its resistance is 3.2 Ω.
Solution
To calculate the length of the wire, we can use the formula for resistance:
R = ρ * (L/A)
where: R is the resistance, ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.
We can rearrange the formula to solve for L:
L = R * (A/ρ)
Substituting the given values:
L = 3.2 Ω * (9.5 x 10^-6 m² / 1.723 x 10^-8 Ω-m)
L = 3.2 Ω * (0.0000095 m² / 0.00000001723 Ω-m)
L = 3.2 Ω * 551.352 m²/Ω
L = 1764.32 m
So, the length of the wire is approximately 1764.32 meters.
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