Three rods $A, B,$ and $C$ of thermal conductivities $K, 2K$ and $4K$, cross-sectional areas $A, 2A$ and $2A$ and lengths $2l, l$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100\,^oC$, $50\,^oC$, and $0\,^oC$ respectively, then the temperature $\theta$ of the junction is
Three rods $A, B,$ and $C$ of thermal conductivities $K, 2K$ and $4K$, cross-sectional areas $A, 2A$ and $2A$ and lengths $2l, l$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100\,^oC$, $50\,^oC$, and $0\,^oC$ respectively, then the temperature $\theta$ of the junction is
- A
$\frac{{300}}{7}\,^oC$
- B
$\frac{{300}}{13}\,^oC$
- C
$\frac{{200}}{7}\,^oC$
- D
$\frac{{200}}{13}\,^oC$
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