A rod CD of thermal resistance 5.0 K/W is joined at the middle of an Identical rod AB as shown in fig. The ends A, B and D are maintained at $100 ° C, 0 ° C$ and $25 ° C$ respectively. Find the heat current in CD.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

6.2 W

4.0 W

2.9 W

8.0 W

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The resistance of the rod $α$ length $R_{A C} = R_{C B} = \frac{R_{C D}}{2} = \frac{5}{2} = 2.5 k w$
Question Image
$H_{1} = \frac{T_{C} - T_{D}}{R_{C D}} = \frac{T_{C} - 25}{5} \to (1)$
$H_{2} = \frac{T_{C} - T_{B}}{R_{C B}} = \frac{T_{C} - 0}{2.5} \to (2)$
$∴ H = \frac{T_{A} - T_{C}}{R_{A C}} = \frac{100 - T_{C}}{2.5}$
$H = H_{1} + H_{2}$
$\frac{100 - T_{C}}{2.5} = \frac{T_{C} - 25}{5} + \frac{T_{C} - 0}{2.5}$ on solving
$T_{C} = 45 ° C$
$∴ H_{1} = \frac{45 - 25}{5} = 4.0 w$