In this L.P.F the input is step signal, I need to find an experssion of Vo(0+) and of Vo(∞).

My answer is:
Vo(0+) = (E*R2)/(R1+R2)
Vo(∞) = E

Am I right?

 

Well, your answer looks good for me.

 

Well, your answer looks good for me.

So in fact the transient is not blocked in this circuit? (Unlike standart L.P.H circuit of capatiance in series to resistor that the transient is blocked)

As we can see in the drawing, there is a transient of E*R2/R1+R2

 

Yes, this circuit will behavior exactly llike you show.

 

This simulation had the step function occurring at t=1 mS.

 

So in fact the transient is not blocked in this circuit? (Unlike standart L.P.H circuit of capatiance in series to resistor that the transient is blocked)

As we can see in the drawing, there is a transient of E*R2/R1+R2

The thing to remember is that a capacitor only forces the voltage across the capacitor to be continuous (while in inductor only forces the current through the inductor to be continuous). The voltages and currents anywhere else are free to change instantly.

 

Hello,

The simple answer here is that the capacitor is a short circuit at t=0 and an open circuit at t=infinity. So either short the cap or open the cap to get the two required results. If you need the actual transition period too then you need to calculate the exponential, but only if you need that also.

In the case where the capacitor has a non zero initial voltage, then you have to replace the capacitor with a battery equal to the initial voltage for the t=0 solution, and again an open circuit for the t=infinity solution.

So all these solutions come from a little topological transformation that just involves the capacitor, which always transforms the circuit into a simple voltage divider or even less, and a little more math for the exponential part but again only if you need that part too.