Question

Two identical conducting rods $A B$ and $C D$ are connected to a circular conducting ring at two diametrically opposite points $B$ and $C$. The radius of the ring is equal to the length of rods $A B$ and $C D$. The area of cross-section, and thermal conductivity of the rod and ring are equal. Points $A$ and $D$ are maintained at temperatures of $100^{\circ} C$ and $0^{\circ} C$. Temperature of point $C$ will be :

• A. $62^{\circ} C$
• B. $37^{\circ} C$
• C. $28^{\circ} C$
• D. $45^{\circ} C$

Answer 1

Answer: (C)

For thermal resistance we use
$R_{A B} =\frac{l}{K A}=R_{C D}$
$\Rightarrow \left(R_{e q}\right)_{B C} =\frac{\pi l}{2 K A}$
We have, $\frac{100-0}{\frac{2 l}{K A}+\frac{\pi l}{2 K A}}=\frac{T_{C}-0}{\frac{l}{K A}}$
$\Rightarrow T_{C} =28^{\circ}$