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I was doing AC circuit analysis using the superposition theorem, which as far as I understand means I can add up the effects of multiple sources by activating only one source at a time (to simplify the analysis instead of considering all at the same time - this is ofcourse when a circuit is linear), but this circuit drew my attention (It is required to find the current in the vertical resistor as a function in time, ignoring first couple of seconds of transience).

Circuit

According to superposition theory I will redraw this circuit 3 times; each time activating a single source at a time, calculate the current for each individual time and then algebraically add them together.

Could I apply superposition theory on two sources at the same time; activating the two same frequency sinusoidal sources together (calculate current in that case using frequency domain analysis), then activating the 10V DC source alone (calculate current using KVL & KCL), So I will only have to redraw the circuit two times and not three.

I did that and got the same answers if I applied the theorem by activating each source alone but I don't know if that is legit or not.

The reason is that I find it easier to solve a circuit with two sources than redrawing the circuit twice and calculating twice. I can be wrong here but this is not the scope of the question :)

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  • \$\begingroup\$ Maybe you should explain what you mean? \$\endgroup\$
    – Andy aka
    Commented Jan 13, 2023 at 16:17
  • \$\begingroup\$ @Andyaka I updated my question to show what I mean in more details. \$\endgroup\$ Commented Jan 13, 2023 at 16:28

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Think of superposition this way. You are not deactivating the other sources, you are setting them to zero output. They are still active, as in a low impedance voltage sources providing a known output voltage, it's just that the output is zero.

Most people replace the other voltage sources with a short circuit, which gives you a low impedance voltage source providing a known output voltage. Which is ultimately the same thing, but from a different point of view.

So as all your voltage sources are active anyway, set them to what ever voltage you feel helps your solution. If you can handle two with finite outputs at the same time, go for it.

We deal with current sources the same way. It doesn't matter whether you 'remove them from the circuit', or set them to zero output current, the effect is the same. Their impedance is infinite, and their output current zero.

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Yes, you can activate two sources at a time in the circuit and set the third source to zero to apply superposition theorem. AC sources use steady state analysis and DC sources require solving integro differential equations. You can superimpose the currents and voltages. They would have a offset which is due to the 10V DC supply. Your final solution would however has a time variable unless the circuit was connected like that for a long time (about 5 to 10 seconds).

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