Question
Three conducting rods of same material and cross-section are shown in figure. Temperatures of$ A, D$ and $C$ are maintained at $20^o C, 90^o C$ and $0^o C$. The ratio of lengths of $BD$ and $BC$ if there is no heat flow in $AB$ is:
✓
Answer
since there is no flow of heat in rod, so temperature of $B$ is equal to temperature at $A$
i.e.,
$\theta_{B}=\theta_{A}=20^{\circ} C$
Heat flowing through $D B$ per second $=$ heat flowing through
i.e., $\frac{K A\left(90^{\circ}-20^{\circ}\right)}{I_{B D}}=\frac{K A\left(20^{\circ}-0^{\circ}\right)}{I_{B C}}$
$\therefore \frac{I_{B C}}{I_{B D}}=\frac{2}{7}$
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