The cross-sectional area of one conductor is 2.5 mm2 and the other is 10 mm2.

| February 11, 2021 | education

The cross-sectional area of one conductor is 2.5 mm2 and the other is 10 mm2. they are made of the same material and the same length. Which of them has less resistance and by how many times.

S1 = 2.5 mm2.

S2 = 10 mm2.

ρ1 = ρ2.

l1 = l2.

R1 / R2 -?

We will assume that the conductor is homogeneous and has a cylindrical shape. The resistance R of a cylindrical homogeneous conductor is determined by the formula: R = ρ * l / S, where ρ is the specific resistance of the material from which the conductor is made, l is the length of the conductor, S is the cross-sectional area of the conductor.

R1 = ρ1 * l1 / S1.

R2 = ρ2 * l2 / S2.

R1 / R2 = ρ1 * l1 * S2 / S1 * ρ2 * l2 = S2 / S1.

R1 / R2 = 10 mm2 / 2.5 mm2 = 4.

Answer: The resistance of a conductor with a cross section of S1 = 2.5 mm2 is 4 times greater than the resistance of a conductor with a cross section of S2 = 10 mm2.



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