An aluminum $(α_{Al} = 4 \times 10^{- 3} /^{0} C)$ wire resistance ‘ $R_{1}$ ’ and carbon wire $(α_{C} = - 0 .5 \times 10^{- 3} /^{0} C)$ resistance ‘ $R_{2}$ ’ are connected in series to have a resultant resistance of 18 ohm at all temperatures . The values of R₁ and R₂ in ohms

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Detailed Solution

Given $α_{Al} = 4 \times 10^{- 3} /^{0} C α_{C} = 0 .5 \times 10^{- 3} /^{0} C$

$R_{1} + R_{2} = 18 Ω, R_{1} α_{Al} = R_{2} α_{C}$
$\frac{R_{1}}{R_{2}} = \frac{α_{C}}{α_{A i}} = \frac{0 .5}{4} = \frac{1}{8} \Rightarrow R_{2} = 8 R_{1}$

$R_{1} + R_{2} = 18 \Rightarrow 9 R_{1} = 18 \Rightarrow R_{1} = 2 Ω, R_{2} = 16 Ω$

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