Three rods $A B, B C$ and $B D$ made of the same material and having the same cross-section have been joined as shown in the figure.
The ends $A, C$ and $D$ are held at temperatures of $20^{\circ} \mathrm{C}, 80^{\circ} \mathrm{C}$ and $80^{\circ} \mathrm{C}$ respectively. If each rod is of same length, then the temperature at the junction $B$ of the three rods is

Question

Three rods $A B, B C$ and $B D$ made of the same material and having the same cross-section have been joined as shown in the figure.

The ends $A, C$ and $D$ are held at temperatures of $20^{\circ} \mathrm{C}, 80^{\circ} \mathrm{C}$ and $80^{\circ} \mathrm{C}$ respectively. If each rod is of same length, then the temperature at the junction $B$ of the three rods is

Aicharya · Accepted Answer

Let the temperature of function $	heta$. Since, $\operatorname{rod} B C$ and $B D$ are parallel to each other (because both having the same temperature difference). Hence, given figure can be redrawn as follows ( $R$ be the resistance of each rod). $\because \frac{Q}{t}=\frac{\left(	heta_1-	heta_2ight)}{R}$ and $\left(\frac{Q}{t}ight)_{A B}=\left(\frac{Q}{t}ight)_{B D}$ $\Rightarrow \frac{(80-	heta)}{R / 2}=\frac{\left(	heta-20^{\circ}ight)}{R} \Rightarrow 	heta=60^{\circ}$

Three rods $A B, B C$ and $B D$ made of the same material and having the same cross-section have been joined…

Solution