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QPages 198-203: Q14: HC Verma: Concepts of Physics - Volume 2 Electric Current in Conductors Pages 198-203: Q14 Solution: The resistance of an iron wire and a copper wire at 20�C are…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently forget that the temperature coefficient formula $R = R_0[1 + \alpha(T - T_0)]$ requires the temperature difference relative to the reference temperature $T_0$ (here $20^\circ\text{C}$), rather than using the absolute temperature $T$ directly. Always substitute $(T - 20)$ into the linear term to ensure the resistance values match the given reference state.

The resistance of an iron wire and a copper wire at 20�C are 3.9 Ω3.9 \ \Omega and 4.1 Ω4.1 \ \Omega, respectively. At what temperature will the resistance be equal? Temperature coefficient of resistivity for iron is 5.0×10−3 K−15.0 \times 10^{-3} \text{ K}^{-1} and for copper, it is 4.0×10−3 K−14.0 \times 10^{-3} \text{ K}^{-1}. Neglect any thermal expansion.

Step-by-Step Verified Solution

**Answer:** T=220�textCT = 220�\\text{C}. **Step-by-Step Explanation:** RFe=3.9(1+5times10−3(T−20))R_{Fe} = 3.9(1 + 5 \\times 10^{-3}(T - 20)), RCu=4.1(1+4times10−3(T−20))R_{Cu} = 4.1(1 + 4 \\times 10^{-3}(T - 20)). Setting equal and solving gives T=220�textCT = 220�\\text{C} [citation:5][citation:12].

All Questions in this Chapter

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