Question

The ratio of thermal conductivity of two rods of different materials is \(4:3\). The two rods have same area of cross-section and same thermal resistance. The lengths of rods are in the ratio

• A. \(5:4\)
• B. \(4:3\)
• C. \(1:5\)
• D. \(7:1\)

Hint:

Thermal resistance is length over (conductivity times area).

Answer 1

The Correct Option is B

Step 1: Set the resistances equal:
$\frac{L_1}{k_1A} = \frac{L_2}{k_2A}$.

Step 2: Rearrange:
$L_1k_2 = L_2k_1$, so $\frac{L_1}{L_2} = \frac{k_1}{k_2} = \frac43$.

Final Answer:
The ratio of lengths is $4:3$, option (B). \[ \boxed{4:3} \]