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Two rods having length $l_{1} and l_{2},$ made of materials with the linear expansion coefficient $α_{1} and α_{2}$ were soldered together. The equivalent coefficient of linear expansion for the combined rod is:

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$\frac{l_{1} α_{2} + l_{2} α_{1}}{l_{1} + l_{2}}$

$\frac{l_{1} α_{2} + l_{2} α_{2}}{α_{1} + α_{2}}$

$\frac{l_{2} α_{1} + l_{1} α_{2}}{α_{1} + α_{2}}$

$\frac{l_{1} α_{1} + l_{2} α_{2}}{l_{1} + l_{2}}$

answer is C.

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$e = Lα (θ ∆); e_{eq} = e_{1} + e_{2} . . . (1) \Rightarrow L_{eq} α_{eq} = L_{1} α_{1} + L_{2} α_{2} \Rightarrow L_{eq} = L_{1} + L_{2} . . . (2)$

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