Six equal resistors, each of value R are joined together as shown in figure

Calculate the equivalent resistance across AB. If a supply of emf `epsilon` is connected across AB, compute the current through the arms DE and AB.

Explanation

The equivalent circuit where resistance R of arm DE is inffectivebecause the wheatstone bridge is balanced. Thus the equivalent circuit reduces to as shown in figure
The equivalent resistance `R_(eq)` across AB is
`1/R_(eq) = 1/(2R) + 1/(2R) + 1/R= 4/(2R) = 2/R or R_(eq) = R/2`
If a battery of emf `epsilon` is connected to AB, then current through arm AB `= epsilon/R_(eq) = epsilon/(R//2) = (2epsilon)/R`
Current through arm `DE =0` (as Wheatstone bridge is in balanced state)