Twelve resistors each of resistance `1 Omega` are connected in the circuit shown in figure. Net resistance between point A and H would be

Options

A. `(5R)/(3)`
B. `(7R)/(6)`
C. `R`
D. `(3R)/(4)`

Answer

D

Explanation

When a cell is conneted across A and C, no current flows in the arms BG and ED due to symmetry in the arrangement. Then equivalent circuit will be as shown in fig. (a) and (b) the effective resistance between A and C is
`(1)/(R_(eff))=(1)/(2R)+(1)/(3R)+(1)/(2R)`
`=(3+2+3)/(6R)=(8)/(6R)=(4)/(3R)` or `R_(eff)=(3R)/(4)`