Question

Two rods of same length, cross sectional area and material transfer a given amount of heat in $12$ seconds, when they are joined in parallel. If they are joined in series with same temperature difference across the ends, then they will transfer same heat in

• A. $24\text{s}$
• B. $3\text{s}$
• C. $1.5\text{s}$
• D. $48\text{s}$

Answer 1

The correct option is D $48\text{s}$

Let the heat transferred be $Q$.

When rods are joined in parallel, heat transferred by rods,
$Q=\frac{k\left(2A\right)\Delta T}{l}\times 12...\left(i\right)$
When rods are joined in series,
$Q=\frac{kA\Delta T}{2l}t...\left(ii\right)$
From Eqs. $\left(i\right)$ and $\left(ii\right)$ we get $t=48\text{s}$.