Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are and . The thermal conductivity of the composite rod will be [2017]

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Q.
Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are $K_{1}$ and $K_{2}$ . The thermal conductivity of the composite rod will be [2017]

1 $\frac{3 (K_{1} + K_{2})}{2}$

2 $K_{1} + K_{2}$

3 $2 (K_{1} + K_{2})$

4 $\frac{K_{1} + K_{2}}{2}$

Ans.
(4)

Equivalent thermal conductivity of the composite rod in parallel combination will be,

$K = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}} = \frac{K_{1} + K_{2}}{2}$

Solution

Q.
Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are $K_{1}$ and $K_{2}$ . The thermal conductivity of the composite rod will be [2017]

1 $\frac{3 (K_{1} + K_{2})}{2}$

2 $K_{1} + K_{2}$

3 $2 (K_{1} + K_{2})$

4 $\frac{K_{1} + K_{2}}{2}$

Ans.
(4)

Equivalent thermal conductivity of the composite rod in parallel combination will be,

$K = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}} = \frac{K_{1} + K_{2}}{2}$

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Solution

Q. Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be [2017]

1 3(K1+K2)2

2 K1+K2

3 2(K1+K2)

4 K1+K22

Ans. (4) Equivalent thermal conductivity of the composite rod in parallel combination will be, K=K1A1+K2A2A1+A2=K1+K22

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Q.
Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are $K_{1}$ and $K_{2}$ . The thermal conductivity of the composite rod will be [2017]

1 $\frac{3 (K_{1} + K_{2})}{2}$

2 $K_{1} + K_{2}$

3 $2 (K_{1} + K_{2})$

4 $\frac{K_{1} + K_{2}}{2}$

Ans.
(4)

Equivalent thermal conductivity of the composite rod in parallel combination will be,

$K = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}} = \frac{K_{1} + K_{2}}{2}$