# In superposition theorem, can I activate multiple sources together?

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).

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 :)

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