Explanation

(c) If a cell is connected between points $A$ and $C$, no current will flow in arms $BE$ and $ED.$ Therefore, the resistance of arms $BE$ and $ED$ an be removed. Now resistance between points $A$ and $C\ $will be the resistance of three parallel arms, each of resistance$= R + R = 2R$
$\therefore$ Total resistance $R_{p}$will be
$\frac{1}{R_{P}} = \frac{1}{2R} + \frac{1}{2R} + \frac{1}{2R} = \frac{3}{2R}\ or\ R_{P} = \frac{2R}{3}$