$12$ wires each of resistance $^{'} r^{'}$ are connected to form a cube. Effective resistance across.

Diagonally opposite corners

= \frac{5 r}{6}

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Face diagonal

= \frac{3 r}{4}

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Two adjacent corners

= \frac{7 r}{12}

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None of these

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Solution

The correct option is A Diagonally opposite corners $= \frac{5 r}{6}$
Effective resistance between $A$ and $E$ is
$r_{e q} = \frac{r}{3} + \frac{r}{6} + \frac{r}{3} = \frac{2 r + r + 2 r}{6} = \frac{5 r}{6}$
Correct option is A

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12 wires each of resistance ′r′ are connected to form a cube. Effective resistance across.

The correct option is A Diagonally opposite corners =5r6Effective resistance between A and E is req=r3+r6+r3=2r+r+2r6=5r6Correct option is A

$12$ wires each of resistance $^{'} r^{'}$ are connected to form a cube. Effective resistance across.

The correct option is A Diagonally opposite corners $= \frac{5 r}{6}$
Effective resistance between $A$ and $E$ is
$r_{e q} = \frac{r}{3} + \frac{r}{6} + \frac{r}{3} = \frac{2 r + r + 2 r}{6} = \frac{5 r}{6}$
Correct option is A