A 200 m long aluminum wire is connected to a current source with a voltage of 1.4 V

| May 17, 2021 | education

A 200 m long aluminum wire is connected to a current source with a voltage of 1.4 V. The current in the conductor is 0.5 A. What is the cross-sectional area of the wire?

L = 200 m.

U = 1.4 V.

I = 0.5 A.

ρ = 0.028 Ohm * mm2 / m.

S -?

Let us express the resistance of the conductor R from Ohm’s law for the section of the circuit: R = U / I, where U is the voltage at the ends of the conductor, I is the current in the conductor.

The resistance R of a cylindrical homogeneous conductor is expressed by the formula: R = ρ * L / S, where ρ is the resistivity of the substance of which the conductor consists, L is the length of the conductor, S is the cross-sectional area.

Since the conductor is made of aluminum, we take the resistivity of aluminum from the table of resistivity of substances: ρ = 0.028 Ohm * mm2 / m.

U / I = ρ * L / S.

S = ρ * L * I / U.

S = 0.028 Ohm * mm2 / m * 200 m * 0.5 A / 1.4 V = 2 mm2.

Answer: The cross-sectional area of ​​the conductor is S = 2 mm2.



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