Question

Two rods of same length, radius and material transfer a given amount of heat in 't' second when they are joined as shown in fig (1). But when they are joined as shown in fig (2) then they will transfer same heat in same condition in time

• A. \(2t\)
• B. \(3t\)
• C. \(4t\)
• D. \(6t\)

Hint:

Parallel doubles the conducting area; series doubles the length. Heat rate ratio is 4.

Answer 1

The Correct Option is C

Step 1: Use thermal resistance:
The thermal resistance of one rod is $R_{th} = \frac{L}{KA}$. Heat flow rate is $\frac{\Delta T}{R_{th}}$.

Step 2: Combine the rods:
Parallel: $R_p = \frac{R_{th}}{2}$. Series: $R_s = 2R_{th}$.

Step 3: Ratio:
The same heat needs times in the ratio of resistances: $\frac{t_s}{t_p} = \frac{R_s}{R_p} = \frac{2R_{th}}{R_{th}/2} = 4$. So $t_s = 4t$.

Final Answer:
The time is 4t, option (C). \[ \boxed{4t} \]