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

$0^{\circ} C$

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${\frac{100}{l}}^{\circ} C$ ; where l is the length of each rod

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

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$100^{\circ} C$

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Solution

The correct option is A
$0^{\circ} C$

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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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

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