The figure shows a tetrahedron where each edg | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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.

Similar Questions

Two resistors are joined in parallel,and their resultant resistance is $\frac{6}{5} \,\Omega$. One of the resistance wires is broken,and the effective resistance becomes $2 \,\Omega$. Then the resistance (in $\Omega$) of the wire that got broken is ..........

$A$ wire of resistance $9 \ \Omega$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be . . . . . . ohm.

$A$ ring is made of a wire having a resistance $R_0 = 12 \,\Omega$. Find the points $A$ and $B$,as shown in the figure,at which a current-carrying conductor should be connected so that the resistance $R$ of the sub-circuit between these points is equal to $\frac{8}{3} \,\Omega$.

Two electric bulbs ($60\,W$ and $100\,W$ respectively) are connected in series. The current passing through them is

Each resistance in the given cubical network has a resistance of $1 \Omega$. The equivalent resistance between points $A$ and $B$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module