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.)

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

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