• # question_answer Three conducting rods of same material and cross-section are connected as shown in figure. Temperatures of $A,\,\,\,D$ and $C$ are maintained at${{20}^{o}}C$, ${{90}^{o}}C$ and${{0}^{o}}C$. If there is no flow of heat in$AB$, then ratio of the lengths of $BC$ and $BD$ is A) $2/9$                                  B) $9/2$ C)  $2/7$                                 D)  $7/2$

Since there is no flow of heat in rod, so temperature of $B$ is equal to temperature at $A\,\,i.e.,$ ${{\theta }_{B}}={{\theta }_{A}}={{20}^{o}}C$ Heat flowing through $DB$ per second                                            = heat flowing through $BC$ per second $i.e.,$ $\frac{KA({{90}^{o}}-{{20}^{o}})}{{{I}_{BD}}}=\frac{KA({{20}^{o}}-{{0}^{o}})}{{{I}_{BC}}}$ $\therefore$  $\frac{{{I}_{BC}}}{{{I}_{BD}}}=\frac{2}{7}$