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I want to find $\Delta V_{ab}$ for the circuit on the figure

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I have tried to use the superposition theorem, and then

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Here I find my first question, because if there is a coil between A and B, then $\Delta V_{ab}=0$ and it not make sense to me in this case... Isn't it? But looking at the solution in some moment the authors write this two circuit

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and I don't understand why they open the circuit in the capacitor branch when there should be a short circuit (I think). Maybe there is some special rule for capacitors and AC source? Maybe in this special case We have to open the circuit in order to don't have a direct coil between the two terminals? or maybe I have missed something...

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The capacitor is an open circuit for dc. As such it is sometimes called a blocking capacitor in equivalent circuits where you need to decouple the dc bias voltages from the ac signals..

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  • $\begingroup$ And what about inductors? I think that they are like a coil for dc... That means that if I want to apply the superposition method for example to a circuit that have two AC sources and one DC source, three capacitors, two inductors and three resistance, then I have to delete one source each time and put then a coil (short circuit), open the circuit in capacitors and current source, and put a coil in each inductor? $\endgroup$
    – user239504
    Commented Feb 21, 2021 at 9:30
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    $\begingroup$ Yes, an ideal inductor would be a short circuit for dc. Assuming everything is linear then superposition should work. $\endgroup$
    – Farcher
    Commented Feb 21, 2021 at 10:00

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