Calculating Rth and τ for a Switched Circuit: A Homework Solution

[ainster31]

Homework Statement

Homework Equations

The Attempt at a Solution

I'm trying to calculate R_th so I can compute τ. The problem is that after the switched is flipped for t>0, here is what is left:

So you would expect R_th to be 3 ohms but it is actually 2 ohms.

Solution for reference:

 

[berkeman]

The circuit you have drawn is for the left side of the circuit after the switch is closed. That part is irrelevant. The part with the time constant is the right side of the circuit, which has just the 2 Ohm resistor and the inductor. After the switch is closed, the two sides of the circuit are independent of each other, because of the short circuit between them.