Answer
The equivalent resistance between points a and b is $54.5~\Omega$
Work Step by Step
We can find the equivalent resistance of the three $100~\Omega$ resistors in series:
$100~\Omega + 100~\Omega + 100~\Omega = 300~\Omega$
We can find the equivalent resistance of the two $100~\Omega$ resistors in series:
$100~\Omega + 100~\Omega = 200~\Omega$
We can find the equivalent resistance of the three values in parallel:
$\frac{1}{R} = \frac{1}{100~\Omega} + \frac{1}{200~\Omega} + \frac{1}{300~\Omega}$
$\frac{1}{R} = \frac{6}{600~\Omega} + \frac{3}{600~\Omega} + \frac{2}{600~\Omega}$
$\frac{1}{R} = \frac{11}{600~\Omega}$
$R = \frac{600~\Omega}{11}$
$R = 54.5~\Omega$
The equivalent resistance between points a and b is $54.5~\Omega$
