# physics

A copper wire has a resistance of 0.425 at 20.0°C, and an iron wire has a resistance of 0.455 at the same temperature. At what temperature are their resistances equal?

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1. Given the temperature coefficients of resistance (α) of each metal at 20°C
copper = 6.8×10^-3[/°C]
iron = 6.51×10^-3[/°C]

Use: R(T+∆T) = R(T) + α R(T) ∆T

Find: (20°C + ∆T) such that:
0.425+0.425×0.0068 ∆T = 0.444+0.425×0.00651 ∆T

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2. I got the solution:

copper=3.9x10^-3
iron=5.0x10^-3

R(1+α∆T)=R(1+α∆T)
0.425(1+0.0039∆T)=0.455(1+0.005∆T)

∆T=-48.6°C
T=20°C-48.6°C=-28.6°C

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3. the length of copper and iron wire is 500m at 0°c. determine the difference in their length at 30°c

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