Question

Consider $$12$$ resistors arranged symmetrically in shape of bi-pyramid $$ABCDEF$$. Here $$ABCD$$ is a square. Point $$E$$, paint $$F$$, and center of square are in the same straight line perpendicular to the plane of square. The resistance of each resistor is $$R$$.
The effective resistance between $$A$$ and $$B$$ is

Answer 1

Correct option is C. $$5R/12$$
Let us remove the resistance between $$A$$ and $$B$$,

then $$E$$ and $$F$$ will be at the same potential, we can draw the remaining as:

$$M$$ is the midpoint of $$DC, M$$ will be at the same pot as $$E$$ and $$F$$.

Now finf $$R_{AB}=5/7R$$.

The resistance which we had removed will be in parallel to it so

$$R_{eq}=\dfrac {R_{AB}R}{R_{AB}+R}=\dfrac {(5/7)RR}{(5/7)R+R}=\dfrac {5}{12}R$$