Answer
The equivalent resistance between points a and b is $183~\Omega$
Work Step by Step
We can find the equivalent resistance $R_1$ of the two $100~\Omega$ resistors in parallel:
$\frac{1}{R_1} = \frac{1}{100~\Omega} + \frac{1}{100~\Omega}$
$\frac{1}{R_1} = \frac{2}{100~\Omega}$
$R_1 = \frac{100~\Omega}{2}$
$R_1 = 50~\Omega$
We can find the equivalent resistance $R_2$ of the three $100~\Omega$ resistors in parallel:
$\frac{1}{R_2} = \frac{1}{100~\Omega} + \frac{1}{100~\Omega} + \frac{1}{100~\Omega}$
$\frac{1}{R_2} = \frac{3}{100~\Omega}$
$R_2 = \frac{100~\Omega}{3}$
$R_2 = 33~\Omega$
The equivalent resistance of $100~\Omega$, $50~\Omega$, and $33~\Omega$ in series is $183~\Omega$
The equivalent resistance between points a and b is $183~\Omega$
