Three rods of identical area of cross-section and made from the same metal form the sides of an isosceles triangle $ABC$, right angled at $B$. The points $A$ and $B$ are maintained at temperatures $T$ and $\sqrt 2 T$ respectively. In the steady state the temperature of the point C is ${T_C}$. Assuming that only heat conduction takes place, $\frac{{{T_C}}}{T}$ is equal to
Three rods of identical area of cross-section and made from the same metal form the sides of an isosceles triangle $ABC$, right angled at $B$. The points $A$ and $B$ are maintained at temperatures $T$ and $\sqrt 2 T$ respectively. In the steady state the temperature of the point C is ${T_C}$. Assuming that only heat conduction takes place, $\frac{{{T_C}}}{T}$ is equal to
- [IIT 1995]
- A
$\frac{1}{{(\sqrt 2 + 1)}}$
- B
$\frac{3}{{(\sqrt 2 + 1)}}$
- C
$\frac{1}{{2(\sqrt 2 - 1)}}$
- D
$\frac{1}{{\sqrt 3 (\sqrt 2 - 1)}}$
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- [IIT 1981]
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