Three rods $A, B,$ and $C$ of thermal conductivities $K, 2K$ and $4K$ and equal, cross-sectional areas 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 $4K$ and equal, cross-sectional areas 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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