Question

An aluminum wire has a resistance of 7.00 Ω at 30.0°C. Determine its resistance (in Ω) at 430°C. The temperature coefficient of resistivity for aluminum wire is 3.90 ✕ 10−3 (°C)−1. (Assume that the temperature coefficient of resistivity was measured using the reference temperature 20°C.)

Answer 1

Answer:

17.92 Ω

Explanation:

R₀ = Initial resistance of the aluminum wire at 30.0°C = 7.00 Ω

R = resistance of the aluminum wire at 430.0°C = ?

α = temperature coefficient of resistivity for aluminum = 3.90 x 10⁻³ °C⁻¹

ΔT = Change in temperature = 430 - 30 = 400 °C

Resistance of the wire is given as

R = R₀ (1 + α ΔT)

R = (7) (1 + (3.90 x 10⁻³) (400))

R = 17.92 Ω