Question

Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities K1, K2, K3,
K 4and K5. When points A and C are maintained at different temperature, no heat flows through the central rod if

(1.)K1=К4 and k2=k3
(2) K1K = K2K3
(3) K1 K2= K3 K4
(4)K1/K4=K2/K3
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Answer 1

Answer:

Answer : K1K2=K3K4

Explanation :

Since no heat flows through the central rod , temperatures at C and D are the same .

The above is like a wheatstone Network .

L1K1A1.L2K2A2=L3K3A3.L4K4A4

L1=L2=L3=L4

A1=A2=A3=A4

K1K2=K3K4

.

Answer 2

Answer:

The correct answer to this question is $K_{1}K_{4} = K_{2}K_{3}$

Explanation:

Given - Five rods of the same dimensions are arranged as shown in the figure. They have thermal conductivities K1, K2, K3, K 4and K5. When points A and C are maintained at different temperatures and no heat flows through the central rod.

To Find - Choose the correct option.

The ratio of the temperature difference between two sides of a material to the rate of heat flow per unit area is known as thermal resistance.

The thermal resistance is given as $R = \frac{L}{KA}$

Now, the concept of a balanced wheat-stone bridge is one in which no stream flows across the middle rod, and it is expressed mathematically as -

$R_{1}R_{4} = R_{2}R_{3}$

And the ratio  $\frac{L}{A}$ is constant.

And we get,

$K_{1}K_{4} = K_{2}K_{3}$

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