why the impedance is a complex quantity

Discussion in 'General Electronics Chat' started by raks_universe, May 3, 2009.

  1. raks_universe

    Thread Starter Active Member

    Mar 15, 2009
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    why we are describing the impedance as a complex quantity and not as a real quantity ?
     
  2. bertus

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  3. PRS

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    Aug 24, 2008
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    It makes the math easier.
     
  4. Papabravo

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    Feb 24, 2006
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    The algebra of complex numbers corresponds to the physical reality of reactive components. Notice that reactance is a real quantity.
     
  5. raks_universe

    Thread Starter Active Member

    Mar 15, 2009
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    Thanks for your replies. but i am not clear about this.
    please explain elaborately .
     
  6. Papabravo

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    In an AC circuit with only resistance, current and voltage are always in phase with each other. When a reactive component is introduced to a circuit, the current and voltage are unable to remain in phase. Now it just so happens that the algebra of complex numbers which has rules for what is a complex number, what operations are allowed, and what are the rules for performing those operations, can be shown to describe the physical reality of what happens in an AC circuit. Was that elaborate enough?

    BTW, Google an Wikipedia are your friends. They have pictures to boot.
    http://www.physclips.unsw.edu.au/jw/AC.html
    http://en.wikipedia.org/wiki/Electrical_impedance
    Read the articles, come back with questions.
     
  7. raks_universe

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    Thank you very much !!!!
     
  8. Papabravo

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    You're welcome
     
  9. KL7AJ

    AAC Fanatic!

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    The best way to grasp this physically is to look at the real part a DISSIPATING power...that is, the generation of heat. (Or, in the case of an antenna, the radiation of power). The imaginary part is the STORAGE of energy. Imaginary or "reactive" energy can be stored in a magnetic field or an electric field. In either case, no energy is lost, merely "sloshed around."

    I think "imaginary" is an unfortunate term, borrowed from the pure math concept. It gives the impression that it is of lesser importance in a physical sense, but it really isn't.

    Hope this helps some.


    Eric
     
  10. Papabravo

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    The important part is that the "algebra" of the imaginary unit "SQRT(-1)" behaves in exactly the correct way to describe the magnitude and the phase of a signal.

    Using the complex exponential notation it might be more intuitive if we called it the "phase part" instead of the imaginary part.
     
  11. PRS

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    Aug 24, 2008
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    Complex numbers are a mathematical tool. The sums and differences of sine waves is made algebraic thereby. In lieu of complex numbers we use trigonometry to add and subtract sinewaves. The math can be very involved and complex, making elaborate use of trigonometric identities. A German, Steinmetz, working for Western Electric (?) in the USA, developed the method of phasors, which uses complex numbers, to greatly simplify the math, reducing it to algebraic manipulation.
     
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