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How do i find the equivalent voltage source?

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data

    How do i find the equivalent voltage source of...

    1) Two AC voltage sources in series with same frequency and phase = ?
    2) One AC voltage source in series with a DC voltage source = ?

    2. Relevant equations

    Equation of a AC voltage source as a function of time [tex]V(t)=V_m * sin( \omega *t + \theta )[/tex]


    3. The attempt at a solution
    1) [tex]V(t)=(V_{m_1}+V_{m_2}) * sin( \omega *t + \theta )[/tex]
    2) [tex]V(t)=(V_{DC}+V_m) * sin( \omega *t + \theta )[/tex]
     
  2. jcsd
  3. Mar 26, 2012 #2

    gneill

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    Staff: Mentor

    Your first answer is correct. The second is not; a DC source is a constant value that does not vary sinusoidally. Suppose you had the two functions f(t) = 4 and g(t) = sin(ωt). What would be the result of adding them: f(t) + g(t) = ?
     
  4. Mar 26, 2012 #3
    since f(t) = 4, then adding g(t) + f(t) would be the same as g(t) + 4...

    Ah that makes sense, if i add a constant function such as DC current to some other non-constant like the sinusoidal function of AC current, it's like adding it's value, so the answer to b) is

    [tex]V(t)=V_{DC}+V_m*sin(\omega *t + \theta)[/tex]
     
  5. Mar 26, 2012 #4

    gneill

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    Staff: Mentor

    Much better! :approve:
     
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