# Should I use superposition if there is a sine wave current source and a DC voltage source in a circuit?

simulate this circuit – Schematic created using CircuitLab

The DC voltage source has an angular frquency of 0 rad/sec.

Do I need to:

1. short circuit the DC voltage source
2. calculate I(t) in time domain
3. open circuit the AC current source
4. calculate I(t)
5. And finally, add the two together

Or can I just do a Kirchoff Voltage Law in the right loop? $$(1.6-0.8j)I+12+(8+4j)I=0$$

This is the original circuit before I simplified the impedance:

• No component should have a complex impedance at DC. Where did you find this circuit example? – The Photon Oct 31 '17 at 2:46
• I added a pic of the original circuits. I just converted them to phasors. – most venerable sir Oct 31 '17 at 3:20
• 1. $\cos 2t$ does not have a frequency of 2 Hz. 2. You need to calculate different equivalent circuits for the capacitors and inductor at DC than at 2 rad/s. – The Photon Oct 31 '17 at 3:30