A wire of cross-sectional area A, length L 1 , resistivity 1 , and temperature coefficient
Question:
A wire of cross-sectional area A, length L1, resistivity ρ1, and temperature coefficient α1 is connected end to end to a second wire of the same cross-sectional area, length L2, resistivity ρ2, and temperature coefficient α2, so that the wires carry the same current.
(a) Show that if ρ1L1α1 + ρ2L2α2 = 0, the total resistance R is independent of temperature for small temperature changes.
(b) If one wire is made of carbon and the other is copper, find the ratio of their lengths for which R is approximately independent of temperature.
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a The total resistance is R 1 A 1 L 1 1 1 T 2 L 2 1 2 T ...View the full answer
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Saptashwa Pal
I had finished my high school at 2014.The same year I was also qualified to appear for Indian National Mathematical Olympiad.And from there, my interest towards mentoring young pupils for learning Mathematics, had grown.I started to aid people in Mathematics from that time.However from 2016 I have also started to provide teaching in Statistics as well which is my major in my Undergraduate studies. I was also selected for interview for M.Stat course in Indian Statistical Institute. From 2018, I initiated my masters studies in Statistics but I lost my enthusiasm and interest in the midway.Nowadays I teach students for their mathematics studies and also aid them in their preparation for math olympiad exams. However I have not put a stop in my studies.This is just a temporary break and I am only saving money to pursue my Master studies (in Mathematics this time) to somewhere better,preferably Europe.
My favourite topics in Mathematics is Number theory,Combinatorics,Linear Algebra ,Analysis and Abstract Algebra.
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