Why does a capacitor offer infinite resistance at steady state?
the circuit conditions for a stable state are either the absence of a change in the circuit current or the absence of current, so that for a capacitor to be in series with a steady-state circuit, it must be either fully charged, or open, which would present an infinite impedance to the circuit.
in practice, a capacitor called dielectric contains very insulating materials with parallel conductive plates, which store the load up to the limit due to the load carried by a low current. but in actual practice the capacitor is an insulator.
The impedance of a capacitor is inversely proportional to the frequency of a signal. you are now talking about the steady state signal. in the case of an alternating signal, the capacitor being connected to a voltage changing periodically, it will continue to charge and discharge, which will maintain the flow of current in the circuit. but for the continuous frequency being 0 the impedance becomes infinite. The capacitor will charge and, once charged, the current will stop flowing.
The replacement state can have several meanings, which means mainly that the applied signal remains in the state where it is, it is the same condition. this could be an alternative 120vac signal.
In this case, the capacitor consists of 2 plates separated by either nothing, air or an insulating material. so it’s open, not a complete driver for the current. once a DC voltage is applied, the capacitor charges and the current stops flowing.
In the case of the alternative AC state, the capacitor would continue to charge and discharge at the alternating signal frequency, then it would appear that a signal is circulating and that it actually is. how much signal depends on the frequency, the higher the frequency, the more the signal will pass.
we often use capacitors to couple the alternating signals while blocking the DC current they could roll on in other words, there could be a DC voltage with an alternating variation and applying this signal to a capacitor would result that the capacitor output would only have the alternative part as with audio. This is why, in some audio circuits, the output is powered by a capacitor, so that only the audio is present at the output.