A copper conductor 130metrrs long hasa resistance of 4.30ohms. If the resistivity of a copper is 1.42*10ohms determine the cross sectional area of the conductor in mmsquared
this would have been easy if you had used the proper units. The resistivity is Ω-m
So, you have
(130m * 14.2Ω-m)/(A m^2) = 4.30Ω
A = 429.3 m^2
That seems unlikely, so I looked up the resistivity of copper, and it is really 1.7*10^-8 Ω-m
Using that, we get
A = 5.139*10^-7 m^2 = 0.513 mm^2, or a diameter of 0.8 mm
That seems quite small, so maybe there are other errors in the question.
To determine the cross-sectional area of the conductor in square millimeters, we can use the formula:
Resistance = (Resistivity * Length) / Cross-sectional Area
Here, we are given:
Resistance = 4.30 ohms
Length = 130 meters
Resistivity (ρ) = 1.42 * 10^(-8) ohms (meters)
We need to solve for the cross-sectional area.
Rearranging the formula, we have:
Cross-sectional Area = (Resistivity * Length) / Resistance
Plugging in the values:
Cross-sectional Area = (1.42 * 10^(-8) ohms (meters) * 130 meters) / 4.30 ohms
Cross-sectional Area ≈ 4.32 * 10^(-7) square meters
To convert this to square millimeters, we need to multiply it by (10^3)², since there are 10^3 millimeters in a meter.
Cross-sectional Area = 4.32 * 10^(-7) * (10^3)² square millimeters
Cross-sectional Area ≈ 432 square millimeters (rounded to the nearest whole number)
Therefore, the cross-sectional area of the copper conductor is approximately 432 square millimeters.