Consider 12 resistor arranged symmetrically in shape of bipyramid ABCDEF. Here ABCD is a square. Point E, point F, and centre of square are in the same straight line perpendicular to the plane of squar. The resistance of each resistor is R.
The effective resistance between E and F is

Options

A. `R//2`
B. `R//3`
C. R
D. none of these

Answer

A

Explanation

If we cannot battery between E and F, then A, B, C, and D will be
all at the same potential. `R_(eq) = (R )/(4) +(R )/(4) = (R )/(2)`
If we connect a battery
between A and C, then E and
F will be at the same potential.
,
Now resistance between DE and EB will be useless. Thus,
`R_(eq) = R//2`
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 follows:
,
M is the midpoint of DC, so M will be at the same spot as E and F.
Now find `R_(AB) = 5//7R.` The resistance that we had removed will be in
parallel to it, so
`R_(eq) = (R_(AB)R)/(R_(AB) +R)= ((5//7)R R)/((5//7)R+R) = (5)/(12)R`