Equivalent resistance 3

The equivalent resistance

$R_{eq}=2R//[R+2R//(R+R)]$

$=2R//(R+2R//2R)$

$=2R//\left( R+\cfrac{2R\times 2R}{2R+2R}\right)$

$=2R//(R+R)$

$=2R//2R$

$=\boxed{R\space \Omega}$

The circuit will have following configurations:

1. One resistance of 2R is in parallel.

2. One resistance of R in parallel connected to two parallel resistors of 2R (R+R) and 2R.

Thus the resultant resistance will be the reciprocal of

$\frac { 1 }{ 2R } \quad +\quad \{ \frac { 1 }{ R\quad +\quad (\frac { 2R\quad x\quad 2R }{ 2R\quad +\quad 2R } ) } \} \quad =\quad \frac { 1 }{ 2R } +\frac { 1 }{ 2R } \quad=\quad \frac { 1 }{ R }$ .

The reciprocal of 1/R is the resultant resistance of the circuit which is R.