Answer
$\tau = 2ms = 2*10^ {-3 }s$
Work Step by Step
capacitors are in parallel therefore equivalent capacitance
$C_{eq} =2\mu F +2\mu F = 4 \mu F $
resistors are in parallel therefore equivalent resistance
$\frac{1}{R_{eq}} = \frac{1}{1k\Omega}+ \frac{1}{1k\Omega}$
$R_{eq} =0.5 k\Omega$
Time constant
$\tau = R_{eq}*C_{eq} =4\mu F * 0.5 k\Omega$
$\tau = 2ms = 2*10^ {-3 }s$
