Question

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

• A. $\frac {2}{3}R$
• B. $\frac {3}{2}R$
• C. $2R$
• D. $\frac {1}{2R}$

Answer 1

Answer: (A)

$\frac {2}{3}R$

Answer 2

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 $R_{AO} = R_{AD} \, and \, R_{OC} = R_{DC},$ resistance $R_{OD}$ becomes ineffective.
So, excluding $R_{BO} \, and \, R_{OD}$ equivalent resistance

$R_{eq}$ of thegiven network between points A and C will be given by,
$\frac {1}{R_{eq}} = \frac {1}{2R} + \frac {1}{2R} + \frac {1}{2R}$
ie, $\, \, \, \, \, \, \, \, \, {R_{eq}} = \frac {2}{3}R$