How to find τ in these circuits?
The arrows on the switches seem to indicate they are opening. I assume (but your problem statement should be more clear about this) that this means the switches are closed for t &lt; 0 and open for t > 0, and you want to solve for the indicated voltages as a function of time for t > 0.

For the 1st one, once you open the switch, there's only one resistor in the circuit, so R is given by its resistance.

For the 2nd one, after the switch opens, there's no current through the 4 kOhm resistor, so you can ignore it. What's the equivalent resistance of the remaining two resistors?