Question

Six identical conducting rods are joined as shown in figure. Points $A$ and $D$ are maintained at temperatures $200^{\circ} C$ and $20^{\circ} C$, respectively. The temperature of junction $B$ will be

• A. $120^{\circ} C$
• B. $100^{\circ} C$
• C. $140^{\circ} C$
• D. $80^{\circ} C$

Answer 1

Answer: (C)

Let the thermal resistance of each rod be $R$.

The two resistances connected along two paths from $B$ to $C$ are equivalent to $2 R$ each and their parallel combination is $R$. Effective thermal resistance between $B$ and $D=2 R$
Temperature of interface $\theta=\frac{R_{1} \theta_{2}+R_{2} \theta_{1}}{R_{1}+R_{2}}$
$\theta=\frac{R \times 20+2 R \times 200}{R+2 R}=\frac{420}{3}=140^{\circ} C$