Determine the resistance and length of a copper wire weighing 89 g and a section of 0.1 mm ^ 2.
| February 16, 2021 | education
S = 0.1 mm2 = 0.1 * 10-6 m2.
ρ “(specific resistance) = 0.017 Ohm * mm2 / m.
ρ (density) = 8900 kg / m3.
R -?
L -?
Since the wire has the shape of a cylinder, its volume V is expressed by the formula: V = S * L.
According to the definition, the density of copper ρ is expressed by the formula: ρ = m / V = m / S * L.
L = m / S * ρ.
We take the density of copper ρ from the table of the density of substances: ρ = 8900 kg / m3.
L = 0.089 kg / 0.1 * 10-6 m2 * 8900 kg / m3 = 100 m.
We express the resistance of the conductor R by the formula: R = ρ “* L / S.
R = 0.017 Ohm * mm2 / m * 100 m / 0.1 mm2 = 17 Ohm.
Answer: the conductor has a resistance R = 17 Ohm and a length L = 100 m.
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