A copper wire has a resistance of 0.425 Ω at 20.0°C, and an iron wire has a resistance of 0.443 Ω at the same temperature. At what temperature are their resistances equal? The temperature coefficient of resistivity for copper is 3.90 10-3(°C)−1 and for iron it is 5.00 10-3(°C)−1.

Their resistances equal at - 12.29°C.

Explanation:

given information:

copper wire's resistance, Ω

iron wire's resistance Ω

coefficient resistivity of copper, αc = 3.90 x 10⁻³ /°C

coefficient resistivity of iron, αi = 5.00 x 10⁻³ /°C

Resistance  at any temperature is

R = [1 + α ΔT], ΔT =

where

R = the resistance of the conductor at the temperature "T"

= conductor resistance at reference temperature

α =  coefficient of resistivity of conductor

T = Temperature

= temperature reference, usually 20°C

At what temperature are their resistances equal?

[1 + αc ΔT] = [1 + αi ΔT]

0.425 [1 + 3.90 x 10⁻³ΔT] = 0.443 [1 + 5.00 x 10⁻³ΔT]

0.425 + 1.6575 x 10⁻³ΔT = 0.443 + 2.215 x 10⁻³ΔT

- 0.018 = 0.5575 10⁻³ ΔT

ΔT = - 32.29°C

ΔT = T -

T = ΔT +

  = - 32.29 + 20

  = - 12.29°C

33: i think it’s b

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