The resistance of 550 m of wire of cross sectional area of 3 mm^2 is 5.5 ohm . Determine the resistivity of the wire. Leave your answer in prefixed engineering notation. (^2 means to the power of 2)
Question
The resistance of 550 m of wire of cross sectional area of 3 mm^2 is 5.5 ohm . Determine the resistivity of the wire. Leave your answer in prefixed engineering notation. (^2 means to the power of 2)
Solution
Sure, to find the resistivity of the wire, we can use the formula for resistance which is:
R = ρL/A
where: R is the resistance, which is 5.5 ohm, L is the length of the wire, which is 550 m, A is the cross-sectional area of the wire, which is 3 mm^2 = 3 x 10^-6 m^2 (since 1 mm^2 = 10^-6 m^2), and ρ is the resistivity of the wire, which we are trying to find.
Rearranging the formula to find ρ gives us:
ρ = RA/L
Substituting the given values into the formula gives us:
ρ = (5.5 ohm * 3 x 10^-6 m^2) / 550 m
Solving this gives us:
ρ = 3 x 10^-8 ohm.m
So, the resistivity of the wire is 3 x 10^-8 ohm.m.
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