Is it possible for this circuit to have two different time constants? One from 0 to 30µs and the other one from 30µs. I tried to calculate the values and I get τ1=20µs and τ2=95/7 µs. They seem quite different so I want someone to confirm or tell me the right way to calculate them.
This is how I did it:
for t=0: S1 in A is closed while in B is open. S2 is open. I tried to find an equivalent circuit formed of a capacitor, a resistance and a voltage source. I got R=10 ohm, C=2µF, V=20V. So τ1 = RC = 10*2µF = 20µs
For t>=30µs: S1 in B is closed and in A is open. S2 is closed. This means that there is no connection between the voltage source and the capacitor. I tried to find an equivalent circuit and I got: R=95/14 ohm, C=2µF V=0V. So τ2 = 95/7 µs.
Now, let's say I already have the capacitor voltage in a period of time (0 - 100µs). How do I calculate the output voltage (Vout(t))? I get two different expressions again...