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Conduction

Five rods of ...

Question

Five rods of the same dimensions are arranged as shown. They have thermal conductivities $k_{1}, k_{2}, k_{3}, k_{4}$ and $k_{5}$ . When points A and B are maintained at different temperatures, no heat flows through the central rod. It follows that :

k_{1} = k_{4}

and

k_{2} = k_{3}

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k_{1} / k_{4} = k_{2} / k_{3}

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k_{1} k_{4} = k_{2} k_{3}

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k_{1} k_{2} = k_{3} k_{4}

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Solution

The correct option is C $k_{1} k_{4} = k_{2} k_{3}$
As we know that thermal resistance is given as: $R = \frac{L}{K A}$
So, simply we apply the concept of balanced wheat-stone bridge for which no current will flow across the central rod,and mathematically it is given as:
$R_{1} R_{4} = R_{2} R_{3}$

Here, ratio of $\frac{L}{A}$ is constant.

Hence, we get the following relation:
$K_{1} K_{4} = K_{2} K_{3}$

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Five rods of the same dimensions are arranged as shown. They have thermal conductivities k1,k2,k3,k4 and k5. When points A and B are maintained at different temperatures, no heat flows through the central rod. It follows that :

Five rods of the same dimensions are arranged as shown. They have thermal conductivities $k_{1}, k_{2}, k_{3}, k_{4}$ and $k_{5}$ . When points A and B are maintained at different temperatures, no heat flows through the central rod. It follows that :