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Two different wirese having lengths L...

Two different wirese having lengths `L_(1)` and `L_(2) ` and respective temperature coefficient of linear expansion `alpha_(1)` and `alpha_(2)` are joined end - to - end . Then the effective temperature coeficient of linear expansion is :

A

`(alpha_1 L_1 + alpha_2 L_2)/(L_1+L_2)`

B

`2 sqrt(alpha_1 alpha_2)`

C

`(alpha_1 +alpha_2)/(2)`

D

`4 (alpha_1alpha_2)/(alpha_1+alpha_2)(L_2L_1)/((L_2+L_1)^2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`At T^@C,L=L_1+L_2`
`At T+DeltaT,L._(eq)=L._1+L._2`
Where `L._1=L_1(1+alpha_1DeltaT)`
`L._2=L_2(1+alpha_2DeltaT)`
`L._(eq)=(L_1+L_2)(1+alpha_(avg)DeltaT)`
`implies (L_1+L_2)(1+alpha_(avg)DeltaT)=L_1+L_2+L_1alpha_1 DeltaT+L_2 alpha_2T`
`implies (L_1+L_2)alpha_(avg)=L_1alpha_1+L_2alpha_2`
`implies alpha_(avg)=(L_1alpha_1+L_2alpha_2)/(L_1+L_2)`
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