The effective resistance between A and B of t | vedclass

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Question

(A) Let the nodes be $A$,$B$,$C$ (top),$D$ (bottom left),$E$ (bottom right),and $F$ (center). The circuit is symmetric about the axis passing through

Vedclass · Accepted Answer

$\frac{8R}{11}$

Vedclass · Answer

(A) Let the nodes be $A$,$B$,$C$ (top),$D$ (bottom left),$E$ (bottom right),and $F$ (center). The circuit is symmetric about the axis passing through the top node $C$ and the center node $F$. By applying symmetry,the potential at the nodes can be analyzed. Let the potential at $A$ be $V_A$ and at $B$ be $V_B$. Due to the symmetry of the circuit,the potential at the top node $C$ is $(V_A + V_B)/2$. Similarly,the potential at the bottom nodes $D$ and $E$ can be determined. By simplifying the circuit using the symmetry principle or by using nodal analysis,we can find the equivalent resistance. For this specific pentagonal network with a central node,the equivalent resistance between $A$ and $B$ is calculated to be $\frac{8R}{11}$.

The effective resistance between $A$ and $B$ of the shown network,where the resistance of each resistor is $R$,is

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