Suppose we make a frame of a regular tetrahedron using six resistors with the same resistance, r and apply a voltage V between point O and point M as shown in the figure. A current I flows into point O and flows out of point M. M is the midpoint of resistor BC

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The current between O and B is $\frac{3}{8} I$ .

The current between A and B is $\frac{I}{8}$ .

The potential at point B is $\frac{2 V}{5}$ .

The equivalent resistance between point O and M is $\frac{5 r}{8}$

answer is A, B, D.

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Detailed Solution

By Kirchoff’s rule,
(1) $r i = r (\frac{I}{2} - i) + r (I - 2 i)$ $\Rightarrow i = \frac{3}{8} I$
$(2) V = \frac{r}{2} \frac{I}{2} + r i = \frac{5}{8} r I$

$R_{e q} = \frac{V}{I} = \frac{5 r}{8}$

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