The effective resistance between points A and C for the network shown figure is

Options

A. `(2)/(3)R`
B. `(3)/(2)R`
C. 2R
D. `(1)/(2R)`

Answer

A

Explanation

As `R_(AB)=R_(AO)` and `R_(BC)=R_(OC)`, so points O and B will be at same potential and hence, resistance `R_(OB)` becomes ineffective. Similarly, as `R_(AO)=R_(AD)` and `R_(OC)=R_(DC)`, resistance `R_(OD)` bcomes ineffective.
So, excluding `R_(BO)` and `R_(OD)`, equivalent resistance `R_(eq)` of the given network between points A and C will be given by,
`(1)/(R_(eq))=(1)/(2R)+(1)/(2R)+(1)/(2R)`
i.e., `R_(eq)=(2)/(3)R`