Question

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

• A. Statement 1 is true but statement 2 is false.
• B. Statement 2 is true but statement 1 is false.
• C. Both statement 1 and statement 2 are true.
• D. Both statement 1 and statement 2 are false.

Answer 1

The correct option is C Both statement 1 and statement 2 are true.

In series combination,
If $A_1=A_2,l_1=l_2$
$k_{eq}=\frac{2k_1{k}_2}{k_1+k_2}$
Since, $k_1=k_2$, we get equivalent thermal conductivity $=k$.
In parallel combination, if $l_1=l_2$ we get
$k_{eq}=\frac{k_1{A}_1+k_2{A}_2}{A_1+A_2}$
Since, $A_1=A_2$ and $k_1=k_2=k$, we get $k_{eq}=k$