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Conduction

The three rod...

Question

The three rods of lenght L and cross-sectional area A is described in the above problem are placed individually, with their ends kept at the same temperature difference. The rate of heat flow through C is equal to the rate of combined heat flow through A and B $k_{c}$ must be equal to

A

k_{A} + k_{B}

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B

\frac{k_{A} k_{B}}{k_{A} + k_{B}}

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C

\frac{1}{2} (k_{A} + k_{B})

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D

2 (\frac{k_{A} k_{B}}{k_{A} + k_{B}})

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Solution

The correct option is A $k_{A} + k_{B}$
As we know that $\frac{Q}{t} = \frac{K A (T_{A} - T_{B})}{L}$ ,and all rods are kept separately,so we write individual equation for all and apply the given relation between them.
$\frac{K_{C} A (T_{1} - T_{2})}{L} = \frac{K_{A} A (T_{1} - T_{2})}{L} = \frac{K_{B} A (T_{1} - T_{2})}{L}$
$K_{C} = K_{A} + K_{B}$

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