Question

Three rods made of the same material having the same cross section have been joined as shown in figure. Each rod is of the same length. The left and right ends are kept at $0^{\circ }\text{C}$ and ${90}^{\circ }\text{C}$ respectively. The temperature of the junction of the three rods will be

• A. ${45}^{\circ }\text{C}$
• B. ${60}^{\circ }\text{C}$
• C. ${30}^{\circ }\text{C}$
• D. ${20}^{\circ }\text{C}$

Answer 1

The correct option is B ${60}^{\circ }\text{C}$

Let $R$ be thermal resistance of each rod,
$\theta$ be temperature at the junction.

$B$ and $C$ are in parallel, hence effective thermal resistance
$R_{BC}^{{}^{\prime }}=\frac{R_1{R}_2}{R_1+R_2}=\frac{R}{2}$ (as $R_1=R_2=R$)

Hence the equivalent circuit diagram is


For the series connection, heat current is same. So,

$\Rightarrow \frac{\theta -0}{R}=\frac{90-\theta }{\frac{R}{2}}\Rightarrow \theta ={60}^{\circ }\text{C}$