Question

Five identical rods are joined as shown in figure. Points $A$ and $C$ are maintained at temperature ${120}^{\circ }C$ and ${20}^{\circ }C$ respectively. The temperature of junction $B$ will be

• A. ${100}^{\circ }$ C
• B. ${80}^{\circ }$ C
• C. ${70}^{\circ }$ C
• D. $0^{\circ }$ C

Answer 1

The correct option is C ${70}^{\circ }$ C

If thermal resistance of each rod is considered $R$ then, the given combination can be redrawn as follows,

From above figure, there are two paths for flow of heat from $B$ to $C$ each having resistance $2R$ and connected in parallel.
Hence, we can deduce that effective resistance between $B$ and $C$ is $R$

As $AB$ and $BC$ are connected in series

$(Thermalcurrent{)}_{AB}=(Thermalcurrent{)}_{BC}$
$\frac{(120-\theta )}{R}=\frac{(\theta -20)}{R}\Rightarrow \theta ={70}^{\circ }C$.