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(A) tetrahedron is a symmetric structure with $4$ vertices $(A, B, C, D)$ and $6$ edges. Each edge has a resistance $r$.Due to the perfect symmetry of

Vedclass · Accepted Answer

$R_{AB} = R_{BD} = R_{BC} = R_{CD} = R_{CA} = R_{AD}$

Vedclass · Answer

(A) tetrahedron is a symmetric structure with $4$ vertices $(A, B, C, D)$ and $6$ edges. Each edge has a resistance $r$.Due to the perfect symmetry of the tetrahedron,the equivalent resistance between any two vertices is the same.Let us calculate the equivalent resistance between two vertices,say $A$ and $B$.When a current enters at $A$ and leaves at $B$,the potential at $C$ and $D$ will be equal due to symmetry.We can connect points $C$ and $D$ with a wire without changing the circuit,or simply note that no current flows between $C$ and $D$ if they were connected.The path $AC$ and $AD$ are in series,and $BC$ and $BD$ are in series.Specifically,the resistance network simplifies to: the edge $AB$ (resistance $r$) is in parallel with the combination of $(AC+CB)$ and $(AD+DB)$.Equivalent resistance $R_{AB} = \frac{r 	imes (r+r)}{r + (r+r)} = \frac{r 	imes 2r}{3r} = \frac{2}{3}r$.Since the tetrahedron is symmetric,the resistance between any two vertices is $\frac{2}{3}r$.Therefore,$R_{AB} = R_{AC} = R_{AD} = R_{BD} = R_{BC} = R_{CD} = \frac{2}{3}r$.Thus,statement $(A)$ is correct.

The figure shows a tetrahedron where each edge has a resistance $r$. Choose the correct statement$(s)$ related to the equivalent resistance between any two vertices.

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