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Question

Two wires of resistance R1 and R2 at 0 C have temperature coefficient of resistance α1 and α2 respectively.These are joined in series.The effective temperature coefficient of resistance is:-

A
α1+α22
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B
α1α2
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C
α1R1+α2R2R1+R2
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D
R1R2α1α2R21+R22
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Solution

The correct option is C α1R1+α2R2R1+R2
R=Rref[1+α(TTref)] where,
R=conductor resistance at temperature T
Rref=conductor resistance at reference temperature e.g 0°C
α=Temperature coefficient of resistance.
Tref=Reference temperature.
When connected in series: R1+R2=R
R1[1+α1(T0)]+R2[1+α2(T0)]=(R1+R2)[1+α(T0)]

R1+R1α1T+R2+R2α2TR1+R2=1+αT

αT=R1+R2+R1α1T+R2α2TR1R2R1+R2
α=R1α1+R2α2R1+R2

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