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Three rods of same dimensions are arrang...


Three rods of same dimensions are arranged as shown in Fig. They have thermal conductivities `K_1`,`K_2` and `K_3`. The points P and Q are maintained at different temeperature for the heat to flow at the same rate along PRQ and PQ. Whi of the following options correct?

A

`K_3=1/2(K_1+K_2)`

B

`K_3=K_1+K_2`

C

`K_3=(K_1K_2)/(K_1+K_2)`

D

`K_3=2(K_1+K_2)`

Text Solution

Verified by Experts

The correct Answer is:
C
H `rarr` heat current

Given, `H_1=H_2`
`implies (KA(T_1-T_2))/(2l)=(K_3A(T_1-T_2))/(l)`
`implies K_3=K/2=(K_1K_2)/(K_1+K_2)` [as `K=(2K_1K_2)/(K_1+K_2)`].
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