Calculate the resistance of 80 metres of copper wire, with a c.s.a. of 0.5mm2, given its resistivity of 1.72 x 10^-6 ohms per metre, Note, the area of the wire must be expressed as a portion of its base unit of measurement, which is the square metre.
To calculate the resistance of the copper wire, we can use Ohm's Law, which states that resistance (R) is equal to the resistivity (ρ) multiplied by the length (L) of the wire, divided by the cross-sectional area (A) of the wire.
The resistivity of copper wire is given as 1.72 x 10^-6 ohms per meter (Ω/m). The length of the wire is 80 meters, and the cross-sectional area is given as 0.5 mm^2.
First, we need to convert the cross-sectional area from mm^2 to m^2. Since 1 mm is equal to 0.001 meters, we can convert the area by multiplying by 0.001^2:
Cross-sectional area (A) = 0.5 mm^2 * (0.001 m/mm)^2 = 0.0000005 m^2
Now that we have the length (L) of the wire as 80 meters and the cross-sectional area (A) as 0.0000005 m^2, we can substitute these values into the formula to find the resistance (R):
Resistance (R) = resistivity (ρ) * length (L) / cross-sectional area (A)
= 1.72 x 10^-6 Ω/m * 80 m / 0.0000005 m^2
= 27.52 Ω
Therefore, the resistance of 80 meters of copper wire with a cross-sectional area of 0.5 mm^2 is 27.52 ohms.