Four identical rods of same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is 100 ∘ C , then the temperature difference between the ends of other diagonal will be Options: A . &nbsp 0 ∘ C B . &nbsp 100 l ∘ C ; where l is the length of each rod C . &nbsp 100 2 l ∘ C D . &nbsp 100 ∘ C

Four identical rods of same material are joined end to end to form a square. If

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Question -

Four identical rods of same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is $100^{\circ}$ C , then the temperature difference between the ends of other diagonal will be

Options:

A .

0^{\circ} C

B .

{\frac{100}{l}}^{\circ} C

; where l is the length of each rod

C .

{\frac{100}{2 l}}^{\circ} C

D .

100^{\circ} C

Answer: Option A
:
A

Suppose temperature difference between A and B is $100^{\circ} C$ and $θ_{A} > θ_{B}$

Heat current will flow from A to B via path ACB and ADB. Since all the rod are identical so $Δ θ)_{A C} = (Δ θ)_{A D}$
(Because heat current $H = \frac{Δ θ}{R}$ ; here R = same for all.)
$\Rightarrow θ_{A} - θ_{C} = θ_{A} - θ_{D} \Rightarrow θ_{C} = θ_{D}$
i.e. temperature difference between C and D will be zero.

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