How to deal with dc source on ac circuits?

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Discussion Overview

The discussion revolves around analyzing AC circuits that include a DC source, specifically focusing on the application of the superposition theorem and phasor analysis. Participants explore methods for determining steady state voltages and currents in the presence of both AC and DC sources.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant describes using the superposition theorem and mesh analysis to find the voltage across a resistor in an AC circuit, yielding a voltage expression of 3.2cos(6t+126.87).
  • Another participant inquires whether phasors have been introduced in the analysis of AC circuits.
  • A participant suggests that the DC current source can be treated as an open circuit for AC analysis due to its infinite output resistance.
  • There is a proposal to short circuit the voltage source to analyze the contribution from the 4A current source, while noting that inductors will behave as short circuits and capacitors as open circuits in steady state.
  • Questions arise about the appropriate frequency to assume for the current source when converting to phasor form.

Areas of Agreement / Disagreement

Participants express differing views on how to handle the DC source in the context of AC analysis, with some suggesting it can be ignored while others propose specific methods for incorporating it into the analysis.

Contextual Notes

There are unresolved assumptions regarding the treatment of the DC source in AC analysis and the implications of using phasor methods. The discussion reflects varying interpretations of circuit behavior in mixed-source scenarios.

Who May Find This Useful

This discussion may be useful for students and practitioners dealing with circuit analysis involving both AC and DC sources, particularly in the context of superposition and phasor techniques.

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Homework Statement
Find the steady state voltage v.
Relevant Equations
v(t) = V(dc) + V(ac)
IMG_20210526_221720.jpg

We are tasked to solve for the steady state voltage v using superposition theorem. I start with solving with voltage source using mesh analysis and got the current flowing through the 3 ohms resistor and get the first value of the voltage which is 3.2cos(6t+126.87). Now my problem is I am confused on how to deal with the other source since we're in ac analysis. I tried solving it with dc analysis but I think it's wrong.
 
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Have you started using Phasors yet or analyzing AC circuits with a single fixed frequency?
 
Yes
 
Great! The 4A current source looks like a/an __________ for AC, so you can probably use the Phasor impedances to write the AC KCL equation(s)...
 
Should I assume w= 0 rad/s for the current source since I'll be needing it to convert it into phasor circuit?
 
Well, I'd just ignore the DC current source for the AC analysis, since an ideal current source has infinite output resistance (looks like an open circuit). Can you write the Phasor KCL equation for the top middle node (since the DC current source is not an open)?
 
IMG_20210526_232911.jpg
 
To get the contribution to v from the 4 amp source just start by short circuiting the voltage source. Now in the steady state the inductors with be short circuits and the capacitor will be an open circuit. You are then left with three parallel circuit elements (one current source and two 4 ohm resistors.) I think you can take it from there.
 

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