Question

the resistance of cu wire and iron wire at 20°c are 4.1 ohm and 3.9 ohm respectively.neglecting any thermal expansion find the temp at which resistance of both are equal [coefficent of thermal expansion of copper is 4*10^-3 &coefficent of themal expansion of iron is 5*10^-3 per kelvin

Answer 1

Given:

Resistance RFe of the iron wire at 20°C = 3.9 Ω

Resistance RCu of the copper wire at 20°C = 4.1 Ω

Temperature coefficient αFe for iron = 5.0 × 10–3 K–1

Temperature coefficient αCu for copper = 4.0 × 10–3 K–1

Let

The temperature at which the resistance be equal = T

Resistance of iron wire at T °C = RFe'

Resistance of copper wire at T °C = RCu'

We know:

R=R0(1+α∆T)

Here, ΔT = T - 20

⇒RFe'=RFe [1+αFe (T−20)]RCu'=RCu [1+αCu (T−20)] RFe'=RCu'⇒RFe [1+αFe (T−20)]=RCu [1+αCu (T−20)]⇒3.9 [1+5×10−3 (T−20)]=4.1 [1+4×10−3 (T−20)]⇒3.9+3.9×5×10−3 (T−20)=4.1+4.1×4×10−3 (T−20)⇒4.1×4×10−3 (T−20)−3.9×5×10−3 (T−20)=−4.1+3.9⇒16.4 (T−20)−19.5 (T−20)=−0.2×103⇒(T−20)(−3.1)=−0.2×103⇒T−20=64.5⇒T=84.

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Answer 2

Answer:

84.51℃

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