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The resistances of an iron wire and a copper wire at 20C are 3.9 Ω and 4.1 Ω respectively. At what temperature will the resistances be equal? Temperature coefficient of resistivity for iron is 5.0 × 10^-3 K^-1 and for copper it is 4.0 × 10^-3 K^-1, Neglect any thermal expansion.

The resistances of an iron wire and a copper wire at 20C are 3.9 Ω and 4.1 Ω respectively. At what temperature will the resistances be equal? Temperature coefficient of resistivity for iron is 5.0 × 10^-3 K^-1 and for copper it is 4.0 × 10^-3 K^-1, Neglect any thermal expansion.

Grade:11

2 Answers

Deepak Patra
askIITians Faculty 471 Points
9 years ago
Sol. R’ base Fe = R base Fe (1 + ∝ base Fe ∆θ), R’ base cu = R base cu (1 + ∝ base Cu ∆θ) R’ base Fe = R base Cu ⇒ R base Fe (1 + ∝ base Fe ∆θ), R base cu (1 + ∝ base Cu ∆θ) ⇒ 3.9 [1 + 5 * 10^-3 (20 - θ)] = 4.1 [1 + 4 * 10^-3 (20 - θ)] ⇒ 3.9 + 3.9 * 5* 10^-3 (20 - θ) = 4.1 + 4.1 * 4* 10^-3 (20 - θ) ⇒ 4.1 * 4 * 10^-3 (20 - θ) – 3.9 * 5 * 10^-3 (20 - θ) = 3.9 – 4.1 ⇒ 16.4 (20 - θ) – 19.5(20 - θ) = 0.2 * 10^3 ⇒ (20 - θ) (-3.1) = 0.2 * 10^3 ⇒ θ - 20 = 200 ⇒ θ = 220°C.
Nishit Bansal
11 Points
5 years ago
∂T=(R0-R')/(R0*α1-R'*α2)
Where ∂T = T-20
After substituting the values and solving we will get 
∂T=64.51
T=64.51+20
T=84.5°C
Which exactly matches with the answer given in HC verma solutions ...thanks hope it helps 

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