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(C) cube has $12$ edges. Let the resistance of each edge be $R$. When we calculate the equivalent resistance between two diagonally opposite corners,t

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$5/6\,R$

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(C) cube has $12$ edges. Let the resistance of each edge be $R$. When we calculate the equivalent resistance between two diagonally opposite corners,the current splits into three paths at the first corner. These three resistors are in parallel,each having resistance $R$,so their equivalent resistance is $R/3$. Then,the current flows through six resistors in parallel,each having resistance $R$,so their equivalent resistance is $R/6$. Finally,the current flows through three resistors in parallel,each having resistance $R$,so their equivalent resistance is $R/3$. The total equivalent resistance $R_{eq}$ is the sum of these series combinations: $R_{eq} = R/3 + R/6 + R/3 = (2R + R + 2R) / 6 = 5R/6$.

Twelve wires of equal length and equal cross-sectional area form a cube. If the resistance of each wire is $R$,then the effective resistance between the two ends of a diagonal is:

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