To solve this problem, let's understand the relationship between heat transfer through rods in series and parallel.
### Given Information:
- Two rods of the same length and material.
- When joined in parallel, they transfer the heat in 12 seconds.
- When joined in series, we need to find the time taken to transfer the same amount of heat.
### Heat Transfer in Parallel:
When rods are joined in parallel, the total heat transfer rate is the sum of the individual rates of heat transfer. If we assume the rate of heat transfer for each rod is \( Q_1 \) and \( Q_2 \), then the total rate \( Q_{\text{total}} \) when the rods are joined in parallel is:
\[
Q_{\text{total}} = Q_1 + Q_2
\]
Since the rods are of the same material and length, the rate of heat transfer for each rod is the same. Hence, if each rod transfers heat at rate \( Q \), the total heat transfer rate in parallel will be \( 2Q \).
Thus, for parallel connection, the time \( t_{\text{parallel}} \) required to transfer a given amount of heat will be:
\[
t_{\text{parallel}} = \frac{Q_{\text{total}}}{Q} = \frac{1}{2} t_{\text{series}} = 12 \, \text{seconds}
\]
### Heat Transfer in Series:
When the rods are joined in series, the total heat transfer rate is lower compared to the parallel case. The total heat transfer rate when the rods are in series is half of the rate when they are in parallel, because the heat has to pass through both rods sequentially, effectively doubling the time taken.
Since the heat transfer rate is halved, the time taken to transfer the same amount of heat will be doubled. Thus, the time required to transfer the same amount of heat in series is:
\[
t_{\text{series}} = 2 \times t_{\text{parallel}} = 2 \times 12 = 24 \, \text{seconds}
\]
### Answer:
The time taken to transfer the same amount of heat when the rods are joined in series is 24 seconds.
Thus, the correct answer is **A. 24 s**.
