A 1.30 m cylindrical rod of diameter 0.550 cm is connected to a power supply that maintains a constant potential difference of 14.0 V across its ends, while an ammeter measures the current through it. You observe that at room temperature (20.0 ∘C) the ammeter reads 18.2 A, while at 92.0 ∘C it reads 17.0 A. You can ignore any thermal expansion of the rod. Part A Find the resistivity and for the material of the rod at 20 ∘C.

Question

Hodges

Physics

6 September, 05:22

A 1.30 m cylindrical rod of diameter 0.550 cm is connected to a power supply that maintains a constant potential difference of 14.0 V across its ends, while an ammeter measures the current through it. You observe that at room temperature (20.0 ∘C) the ammeter reads 18.2 A, while at 92.0 ∘C it reads 17.0 A. You can ignore any thermal expansion of the rod. Part A Find the resistivity and for the material of the rod at 20 ∘C.

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Answers (1)

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Butler · Answer 1

1.41 * 10⁻⁵Ωm

Explanation:

Resistance of wire is defined by the formula

R = ρL / A

RA / L = ρ

using ohm's law

V = IR

R at 20°C = V / I = 14 / 18.2 = 0.769 ohms

RA / L = ρ

diameter = 0.55 cm = 0.55 / 100 in m = 0.0055 m

A = πr² = 3.142 * (0.0055 m / 2) ² = 0.0000238 m²

ρ = (0.769 ohms * 0.0000238 m²) / 1.30 m = 1.41 * 10⁻⁵Ωm