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(D) tetrahedron has $4$ vertices and $6$ edges. Let the vertices be $A, B, C, D$. If a battery is connected between any two vertices (say $A$ and $B$)

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All of the above

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(D) tetrahedron has $4$ vertices and $6$ edges. Let the vertices be $A, B, C, D$. If a battery is connected between any two vertices (say $A$ and $B$),the circuit exhibits symmetry.Due to the symmetry of the tetrahedron,the potential at the other two vertices ($C$ and $D$) will be equal. Thus,no current flows through the branch $CD$ because there is no potential difference between $C$ and $D$.Since the potential at $C$ and $D$ is the same,we can treat them as a single node or remove the branch $CD$ without affecting the circuit. The equivalent resistance between any two vertices of a tetrahedron with edge resistance $r$ is $R_{eq} = r/2$.Since the equivalent resistance is the same regardless of which two vertices the battery is connected to,the current drawn from the battery $(I = V/R_{eq})$ will also be the same in each case.Therefore,all the given statements are correct.

The figure shows a tetrahedron where each edge has a resistance $r$. If a battery is connected between any two vertices of the tetrahedron,identify the correct statement$(s)$.

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