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Three identical rods A,B and C are place...

Three identical rods A,B and C are placed end to end. A temperature difference is maintained between the free ends of A and C. The thermal conductivity of B is `thrice` that of C and `half` of that of A. The effective thermal conductivity of the system is ........... (`K_A` is the thermal conductivity of rod A).

A

`1/3K_(A)`

B

`3K_(A)`

C

`2K_(A)`

D

`(2)/(3)K_(A)`.

Text Solution

Verified by Experts

The correct Answer is:
A

Given, `K_(B)=K_(A)//2`
and `K_(B)=3K_(C)`
`:.K_(C)=K_(A)//6`
Rods are in series from so
`(L)/(K)=(l_(1))/(K_(A))+(l_(2))/(K_(B))+(l_(3))/(K_(C ))" "(becausel=l_(1)=l_(2)=l_(3))`
`(3l)/(K)=(l)/(K_(A))+(l)/(K_(1)//2)+(l)/(K_(A)//6)`
or `(3l)/(K)=(9l)/(K_(A))`
or `K=(K_(A))/(3)`
So, correct choice is (a).
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