I know capacitors only work as impedance in AC circuit with the formula Xc=1/wC and thus in DC capacitors are an open circuit once charged

But my question is about a capacitor in a pulsating DC circuit, it is not AC so you are not allowed to use the Xc formula but in a pulsating DC there's a frecuency so maybe you could use that formula or a similar one.

What I mean is to calculate Xc in this circuit you use the formula Xc=1/wC



but what formula you have to use to calculate Xc in this circuit (if you can talk about Xc in this case)?

 

Homework?

 

what formula you have to use to calculate Xc in this circuit (if you can talk about Xc in this case)?

You can't/don't use Xc since pulsating DC contains many Fourier frequencies.

You can use the charge movement through a capacitor due to the rate-of-change of the DC voltage and the capacitor size to determine the momentary current (example LTspice sim below):

Note that if there's a diode in series with the capacitor (as the second circuit seems to show) then it will charge up to a fixed voltage, since there is no path for it to discharge..