Two A.C Sources in one circuit. Magnitude and Frequency the same but one is Sin function + one Cos.

Discussion in 'Homework Help' started by Neil Hayes, Apr 1, 2016.

  1. Neil Hayes

    Thread Starter New Member

    May 23, 2015
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    Hi there folks!

    I'm just doing a question at the moment and the question asks to find the current through a load which is being fed from two voltage sources via their respective reactances ( inductive ). I need to find this current through a center branch using three different techniques which isn't an issue. My am just slightly confused by the fact that the voltages are quoted with respect to time and are also different functions, for eg: 415sin(100pit) and 415cos(100pit)

    There is no mention of time so would I be correct to assume that I just take the magnitude in each case and assume that it is giving an out of that constantly?

    Any help would be greatly appreciated : )

    Neil
     
    Last edited: Apr 1, 2016
  2. WBahn

    Moderator

    Mar 31, 2012
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    No assumption needed -- you have the functions.

    Have you learned about phasors yet?
     
  3. Neil Hayes

    Thread Starter New Member

    May 23, 2015
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    Thanks a million for your reply WBahn!

    I sure did do phasors. The sine function will be 0 degrees in polar with magnitude 415 and the cosine will lead by 90 degrees, is that the right approach? I had a brain freeze on that question!
     
  4. WBahn

    Moderator

    Mar 31, 2012
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    4,800
    You got it. Good luck.
     
    Neil Hayes likes this.
  5. Neil Hayes

    Thread Starter New Member

    May 23, 2015
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    Hi WBahn,

    Sorry for the delayed response here but one thing I've noticed on this question is that it quotes that the system is acting with a (.7 p.f. Lagging).

    The question asks to find the current through a particular load. I'm not being asked anything about the power dissipated or anything like that so I'm not sure of the relevance of the p.f.

    Maybe it's there to cause confusion? If so it is working lol

    Neil
     
  6. MrAl

    Well-Known Member

    Jun 17, 2014
    2,439
    492
    Hello,

    It would be better if you showed the circuit.

    There are different ways to handle this depending on the circuit.
    Sine and cosine functions can add to form one function sometimes. Other times we can just handle it as a two source circuit using superposition.
     
    Neil Hayes likes this.
  7. Neil Hayes

    Thread Starter New Member

    May 23, 2015
    14
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    Hi there MrAI,

    Thanks for your reply. I've actually just figured it out there this morning. Being told the p.f. enabled me to break the 50ohm load into its real and imaginary parts. I took the arccos of .70 which gave me the phase angle and this let me find the resistance and reactance of the load.

    Thanks for getting back to me!

    Neil
     
  8. MrAl

    Well-Known Member

    Jun 17, 2014
    2,439
    492
    Hi,

    Congrats :)

    Sometimes it is nice to see the circuit anyway even if already solved, for the benefit of other readers who might be working on the same problem.
     
    Neil Hayes likes this.
  9. Neil Hayes

    Thread Starter New Member

    May 23, 2015
    14
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    Hi MrAI,

    Here's the question and the circuit diagram: 2016-04-27 12.40.08.jpg
     
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