Twelve wires of equal length and same cross-s | vedclass

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(C) To find the equivalent resistance between two diagonally opposite corners of a cube,we can use the symmetry of the circuit.Let the current $I$ ent

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$\frac{5}{6}R$

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(C) To find the equivalent resistance between two diagonally opposite corners of a cube,we can use the symmetry of the circuit.Let the current $I$ enter at corner $A$ and leave at corner $D$.At node $A$,the current splits equally into $3$ branches,each with resistance $R$. The equivalent resistance of these $3$ parallel resistors is $R/3$.From these $3$ nodes,the current further splits into $6$ branches,each with resistance $R$. The equivalent resistance of these $6$ parallel resistors is $R/6$.Finally,the current converges through $3$ branches,each with resistance $R$,connected to the exit node $D$. The equivalent resistance of these $3$ parallel resistors is $R/3$.Since these three sets of resistors are in series,the total effective resistance $R_{eq}$ is:$R_{eq} = \frac{R}{3} + \frac{R}{6} + \frac{R}{3} = \frac{2R + R + 2R}{6} = \frac{5R}{6}$

Twelve wires of equal length and same cross-section are connected in the form of a cube. If the resistance of each of the wires is $R$,then the effective resistance between the two diagonal ends would be

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