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Thermal Resistance

Statement 1 :...

Question

Statement 1 : Equivalent thermal conductivity of two rods of same physical dimensions and having same thermal conductivity $(k)$ connected to each other in parallel combination is equal to $k$ .
Statement 2 : Equivalent thermal conductivity of two rods of same physical dimensions and having same thermal conductivity $(k)$ , connected to each other in series combination is equal to $k$ .

A

Statement 1 is true but statement 2 is false.

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B

Statement 2 is true but statement 1 is false.

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C

Both statement 1 and statement 2 are true.

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D

Both statement 1 and statement 2 are false.

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Solution

The correct option is C Both statement 1 and statement 2 are true.
In series combination,
If $A_{1} = A_{2}, l_{1} = l_{2}$
$k_{e q} = \frac{2 k_{1} k_{2}}{k_{1} + k_{2}}$
Since, $k_{1} = k_{2}$ , we get equivalent thermal conductivity $= k$ .
In parallel combination, if $l_{1} = l_{2}$ we get
$k_{e q} = \frac{k_{1} A_{1} + k_{2} A_{2}}{A_{1} + A_{2}}$
Since, $A_{1} = A_{2}$ and $k_{1} = k_{2} = k$ , we get $k_{e q} = k$

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Thermal Resistance

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