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Question

A wire of cross-section area A, length L1, resistivity ρ1 and temperature coefficient of resistivity α1 is connected to a second wire of length L2, resistivity ρ2 , temperature coefficient of resistivity α2 and the same area A, so that wire carries same current. Total resistance R is independent of temperature for small temperature change if (Thermal expansion effect is negligible)

A
α1α2
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B
ρ1L1α1+ρ2L2α2=0
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C
L1α1+L2α2=0
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D
None
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Solution

The correct option is C ρ1L1α1+ρ2L2α2=0
R1=P10L1Aα1
R2=P20L2Aα2
Req=R1+R2
Req(1+αΔT)=R1(1+α1ΔT)+R2(1+α2ΔT)=R1+R2
R1α1ΔT=R2α2ΔT=v
R1α1=R2α2
R1L1Aα1=α2ρ2L2A
α1L1ρ1+α2ρ2 L2=0

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