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In a circuit in steady state is it possible to have a compensating wave? My understanding of a compensating wave is that it is there when a switch is switched. It provides a voltage and current that is the negative of what is so that KCL is obeyed whilst the current flows into the negative of the source.

schematic

simulate this circuit – Schematic created using CircuitLab

For example, if this switch had just been opened, I would say that there is a compensating wave to make the voltage and current to the right of SW1 equal to zero otherwise current would be leaving the junction but not entering.

So my question is can there be a compensating wave in steady state? My intuition says no since there is no change to compensate like in the circuit with the switch.

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By definition steady state means the system has settled down after a sufficient amount of time to it's normal state.

There is no memory in this system, so talking about system dynamics is not useful. If there were a capacitor or inductor, you could start to talk about the dynamics of the system and its state.

In this system the state is either on or off, there is no in between.

If you had drawn a real switch instead of an ideal switch, then you could also consider switch bounce (where the inductance of the switch and parasitic capacitance elsewhere in the system causes oscillations).

So to answer your question:

So my question is can there be a compensating wave in steady state? My intuition says no since there is no change to compensate like in the circuit with the switch.

In this circuit there are no 'waves', it's either on or off.

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