Answer
The equivalent resistance between points a and b is $~14~\Omega$
Work Step by Step
We can find the equivalent resistance of the $60~\Omega$ and $40~\Omega$ resistors in parallel:
$\frac{1}{R} = \frac{1}{60~\Omega} + \frac{1}{40~\Omega}$
$\frac{1}{R} = \frac{2}{120~\Omega} + \frac{3}{120~\Omega}$
$\frac{1}{R} = \frac{5}{120~\Omega}$
$R = \frac{120~\Omega}{5}$
$R = 24~\Omega$
We can find the equivalent resistance of the $60~\Omega$, $60~\Omega$, and $45~\Omega$ resistors in parallel:
$\frac{1}{R} = \frac{1}{60~\Omega} + \frac{1}{60~\Omega} + \frac{1}{45~\Omega}$
$\frac{1}{R} = \frac{3}{180~\Omega} + \frac{3}{180~\Omega} + \frac{4}{180~\Omega}$
$\frac{1}{R} = \frac{10}{180~\Omega}$
$R = \frac{180~\Omega}{10}$
$R = 18~\Omega$
The equivalent resistance of the left section of the circuit is $24~\Omega+18~\Omega$ which is $42~\Omega$
We can find the equivalent resistance of $42~\Omega$ and $21~\Omega$ resistors in parallel:
$\frac{1}{R} = \frac{1}{42~\Omega} + \frac{1}{21~\Omega}$
$\frac{1}{R} = \frac{1}{42~\Omega} + \frac{2}{42~\Omega}$
$\frac{1}{R} = \frac{3}{42~\Omega}$
$R = \frac{42~\Omega}{3}$
$R = 14~\Omega$
The equivalent resistance between points a and b is $~14~\Omega$
