Hree rods of same dimensions are arranged as shown in figure they have thermal conductivities {K₁}

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10-2.Transmission of Heat

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hree rods of same dimensions are arranged as shown in figure they have thermal conductivities ${K_1},{K_2}$ and${K_3}$ The points $P$ and $Q$ are maintained at different temperatures for the heat to flow at the same rate along $PRQ$ and $PQ$ then which of the following option is correct

A

${K_3} = \frac{1}{2}({K_1} + {K_2})$

B

${K_3} = {K_1} + {K_2}$

C

${K_3} = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}}$

D

${K_3} = 2({K_1} + {K_2})$

Solution

(c) The given arrangement of rods can be redrawn as follows

It is given that $H_1$ = $H_2$

==> $\frac{{KA({\theta _1} – {\theta _2})}}{{2l}} = \frac{{{K_3}A({\theta _1} – {\theta _2})}}{l}$

==> ${K_3} = \frac{K}{2} = \frac{{{K_1}{K_2}}}{{{K_1} + {K_2}}}$

Standard 11

Physics

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