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Question

Two resistors with temperature coefficients of resistance α1 and α2 have resistances R1 and R2 at 0C. What is the temperature coefficient of the compound resistor consisting of the two resistors connected in parallel?


A

R1α1+α2R2R1+R2

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B

α1+α22

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C

2α1+α2α1+α2

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D

α1R2+α2R1R1+R2

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Solution

The correct option is D

α1R2+α2R1R1+R2


When connected in parallel,
1R=1R1+1R2
Differentiating both sides,
dRR2=dR1R21+dR2R22αRdTR2=α1R1dTR21+α2R2dTR22αR=α1R1+α2R2α=R(α1R1+α2R2)=R1R2R1+R2(α1R2+α2R1R1R2)α=α1R2+α2R1R1+R2


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