# Total response of a first order RC circuit

I need to find the step response (steady-state + natural response) of the given RC circuit. The step is at t = 0 secs, that is,

where Vp is a constant.

I found the time constant to be

I am stuck at finding at final voltages across the capacitors. I open-circuited both the capacitors but then realized that middle voltage can be arbitrary.

• How did you find the time constant? Please elaborate. You can find the final voltage using the equation from which you found the time constant. Commented Jul 19, 2019 at 7:12
• @Huisman I didn't write the differential equation but just evaluated it intuitively. Since the 2 capacitors are in series. Commented Jul 21, 2019 at 3:55

At the steady state there will be no current flowing because the capacitor is an open circuit for DC. Then your voltage accross the resistor will be 0.

So Vp is distributed accross both capacitors. But because these capacitors are in series, they will have the same charge.

So basically you have: Q = C1.V1 = C2.V2 and V1 + V2 = Vp

From these two equations you can then compute V1 and V2.