Answer:
Their resistances equal at - 12.29°C.
Explanation:
given information:
copper wire's resistance, [tex]R_{c} =0.425[/tex] Ω
iron wire's resistance [tex]R_{i} =0.443[/tex] 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 = [tex]R_{ref}[/tex] [1 + α ΔT], ΔT = [tex]T - T_{ref}[/tex]
where
R = the resistance of the conductor at the temperature "T"
[tex]R_{ref}[/tex] = conductor resistance at reference temperature
α = coefficient of resistivity of conductor
T = Temperature
[tex]T_{ref}[/tex] = temperature reference, usually 20°C
At what temperature are their resistances equal?
[tex]R_{c}[/tex] [1 + αc ΔT] = [tex]R_{i}[/tex] [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 - [tex]T_{ref}[/tex]
T = ΔT + [tex]T_{ref}[/tex]
= - 32.29 + 20
= - 12.29°C
