Answer
The equivalent resistance between points a and b is $40~\Omega$
Work Step by Step
The equivalent resistance of the $10~\Omega$ and $40~\Omega$ resistors in series is $50~\Omega$
The equivalent resistance of the $55~\Omega$ and $20~\Omega$ resistors in series is $75~\Omega$
We can find the equivalent resistance $R_p$ of resistors in parallel:
$\frac{1}{R_p} = \frac{1}{50~\Omega} + \frac{1}{75~\Omega}$
$\frac{1}{R_p} = \frac{3}{150~\Omega} + \frac{2}{150~\Omega}$
$\frac{1}{R_p} = \frac{5}{150~\Omega}$
$R_p = \frac{150~\Omega}{5}$
$R_p = 30~\Omega$
The equivalent resistance of $30~\Omega$ and the $10~\Omega$ resistor in series is $40~\Omega$
The equivalent resistance between points a and b is $40~\Omega$
