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Two rods A and B of different materials ...

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are `K_(1)` and `K_(2)`. The thermal conductivity of the composite rod will be

A

`(3(K_(1)+K_(2)))/(2)`

B

`K_(1)+K_(2)`

C

`2(K_(1)+K_(2))`

D

`(K_(1)+K_(2))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Thermal resistance `(R)=(kA)/(l)`
`R_("eq")=(R_(1)R_(2))/(R_(1)+R_(2))`
`(because` for parallel)
`l/(2k_("eq")A)=l/(k_(1)A)+l/(k_(2)A)`
Thermal resistance `(R)=l/(kA)`
Rods are in parallel combination
`R_("eq")=(R_(1)R_(2))/(R_(1)+R_(2))`
`l/(K_("eq")(2A))=(l/(K_(1)A)*l/(K_(2)A))/(l/(K_(1)A)+l/(K_(2)A))=(1/(K_(1)K_(2))l/(A))/(1/(K_(1))+1/(K_(2)))`
`=(1/(K_(1)K_(2))l/(A))/((K_(1)+K_(2))/(K_(1)K_(2)))=1/((K_(1)+K_(2)))l/(A)`
`rArrK_("eq")=(K_(1)+K_(2))/(2)`
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