A square is formed by four identical rods. If | vedclass

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(A) Let the four identical rods form a square $ABCD$,where $AC$ and $BD$ are the diagonals.Let the temperature at point $A$ be $T_{A} = T^{\circ}C$ an

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$0^{\circ}C$

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(A) Let the four identical rods form a square $ABCD$,where $AC$ and $BD$ are the diagonals.Let the temperature at point $A$ be $T_{A} = T^{\circ}C$ and at point $C$ be $T_{C} = T + 100^{\circ}C$.Since the rods are identical,the thermal resistance of each rod is the same,say $R$.Heat flows from $A$ to $C$ through two parallel paths: path $ABC$ and path $ADC$.For path $ABC$,the temperature at $B$ is the midpoint of the potential drop between $A$ and $C$ because the resistances of $AB$ and $BC$ are equal.$T_{B} = \frac{T_{A} + T_{C}}{2} = \frac{T + (T + 100)}{2} = T + 50^{\circ}C$.Similarly,for path $ADC$,the temperature at $D$ is the midpoint of the potential drop between $A$ and $C$.$T_{D} = \frac{T_{A} + T_{C}}{2} = \frac{T + (T + 100)}{2} = T + 50^{\circ}C$.The temperature difference across the diagonal $BD$ is $\Delta T_{BD} = |T_{B} - T_{D}| = |(T + 50) - (T + 50)| = 0^{\circ}C$.

$A$ square is formed by four identical rods. If the temperature difference across one diagonal is $100^{\circ}C$,what will be the temperature difference across the other diagonal?

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