wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The resistance of an iron wire and a copper wire at 20°C are 3.9 Ω and 4.1 Ω, respectively. At what temperature will the resistance 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.

Open in App
Solution

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+αT)
Here, ΔT = T - 20
RFe'=RFe 1+αFe T-20RCu'=RCu 1+αCu T-20 RFe'=RCu'RFe 1+αFe T-20=RCu 1+αCu T-203.9 1+5×10-3 T-20=4.1 1+4×10-3 T-203.9+3.9×5×10-3 T-20=4.1+4.1×4×10-3 T-204.1×4×10-3 T-20-3.9×5×10-3 T-20=-4.1+3.916.4 T-20-19.5 T-20=-0.2×103T-20-3.1=-0.2×103T-20=64.5T=84.5 °C

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon