Answer
The equivalent resistance is $~~3.13~\Omega$
Work Step by Step
The equivalent resistance of two resistors in series is $2R$
We can find the equivalent resistance $R_{tm}$ of the top branch and the middle branch which are in parallel:
$\frac{1}{R_{tm}} = \frac{1}{2R}+\frac{1}{R}$
$\frac{1}{R_{tm}} = \frac{1}{2R}+\frac{2}{2R}$
$R_{tm} = \frac{2R}{3}$
These two branches are in series with the right part of the bottom branch. This equivalent resistance is $ \frac{2R}{3}+R$ which is $\frac{5R}{3}$
This is in parallel with the left part of the bottom branch.
We can find the equivalent resistance:
$\frac{1}{R_{eq}} = \frac{1}{R}+\frac{1}{5R/3}$
$\frac{1}{R_{eq}} = \frac{1}{R}+\frac{3}{5R}$
$\frac{1}{R_{eq}} = \frac{5}{5R}+\frac{3}{5R}$
$\frac{1}{R_{eq}} = \frac{8}{5R}$
$R_{eq} = \frac{5R}{8}$
$R_{eq} = \frac{(5)(5.00~\Omega)}{8}$
$R_{eq} = 3.13~\Omega$
The equivalent resistance is $~~3.13~\Omega$
