Two resistances R1 and R2 are made of different materials. The temperature coefficient of the material of R1 is a and of the material of R2 is −β. The resistance of the series combination of R1 and R2 will not change with temperature, if R1/R2 equals

R1+R2=R1 1+αt + R2 1−βt⇒R1+R2=R1 +R2+R1αt−R2βt⇒ R1R2=βα

Two resistances R1 and R2 are made of different materials. The temperature coefficient of the material of R1 is a and of the material of R2 is −β. The resistance of the series combination of R1 and R2 will not change with temperature, if R1/R2 equals

R1+R2=R1 1+αt + R2 1−βt⇒R1+R2=R1 +R2+R1αt−R2βt⇒ R1R2=βα

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Two resistances R₁ and R₂ are made of different materials. The temperature coefficient of the material of R₁ is a and of the material of R₂ is $- β$ . The resistance of the series combination of R₁ and R₂ will not change with temperature, if R₁/R₂ equals

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$\frac{α}{β}$

$\frac{α + β}{α - β}$

$\frac{α^{2} + β^{2}}{α β}$

$\frac{β}{α}$

answer is D.

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$\begin{array}{l} R_{1} + R_{2} = R_{1} (1 + αt) + R_{2} (1 - βt) \\ \Rightarrow R_{1} + R_{2} = R_{1} + R_{2} + R_{1} αt - R_{2} βt \Rightarrow \frac{R_{1}}{R_{2}} = \frac{β}{α} \end{array}$

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Two resistances R1 and R2 are made of different materials. The temperature coefficient of the material of R1 is a and of the material of R2 is −β. The resistance of the series combination of R1 and R2 will not change with temperature, if R1/R2 equals

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Two resistances R₁ and R₂ are made of different materials. The temperature coefficient of the material of R₁ is a and of the material of R₂ is $- β$ . The resistance of the series combination of R₁ and R₂ will not change with temperature, if R₁/R₂ equals