How can the resistance of a conductor change if its longitude is increased by 2 times, and its diameter by 4 times?

Conductor resistance can be calculated using the formula:

R = ρ * l / S, where ρ is the resistivity of the conductor material, l is the length of the conductor, S is the cross-sectional area.

Before increasing the length and diameter:

R1 = ρ * l1 / S1, where S1 = 0.25ΠD12.

After increasing the length and diameter:

R2 = ρ * l2 / S2, where l2 = 2l1, S2 = 0.25ΠD22, D2 = 4D1.

R2 / R1 = (ρ * l2 / S2) / (ρ * l1 / S1) = (ρ * 2l1 / 0.25Π (4D1) 2) / (ρ * l1 / 0.25ΠD12) = 2/16 = 1 / eight.

Answer: The resistance of the conductor will decrease by 8 times.

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