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about electric reactances

manojk peradka
Intellectual 300 points


why reactances are always imaginary??searched for the same in so many websites......but no answer satisfied me well....moreover none has explained it well,........pls anyone explain actual reason why should we represent it by imaginary ????with proof .......

  • 0
    Expert 1480 points

    Hello,

    this topic is a little bit off topic.

    But the origin of complex numbers in electronics and other scientific directions is to solve the equation x2+1 = 0

    http://en.wikipedia.org/wiki/Complex_number

    Regards Marco

  • 0 in reply to Marco
    Intellectual 300 points

    hello,

    i agree that complex numbers are originated from equations such as x2+1=0......but what is the proof behind taking reactances as imaginary???actually am really interested in mathematical proof of it..........

  • 0 in reply to manojk peradka
    Guru 58965 points

    In a sense, all numbers are “imaginary”. For that matter, all human knowledge can be called “imaginary” ;)

    Seriously, electrical impedance has two dimensions and cannot be expressed by a single one-dimensional quantity. Using complex numbers is a convenient way to describe impedance. By convention, the real component of this complex number represents resistance. The imaginary component represents reactance. Thus reactance being imaginary is just the result of our convention. We could have used the real part as reactance and the imaginary part as resistance. We could have used a two-dimensional vector instead of a complex number too (and forget about real vs. imaginary).

  • 0
    Guru 227245 points

    manojk peradka said:
    why reactances are always imaginary

    To put it in simplified words: For Reactances, curent and voltage are out-of-phase. (contrary to resistances wher ethey are in-phase). Being out-of-phase electrically means being imaginary mathematically. Everything that elaves the straight "number-ray" of real numbers has an imaginary component.
    Like everything that leaves the straight path of reality belongs to imagination.

    manojk peradka said:
    with proof

    It's the definition. If things are defined one way, there is no proof needed :) If reactances weren't imaginary, the weren't reactances but resistanes instead.

  • 0 in reply to Jens-Michael Gross
    Guru 35595 points

    It's  just a convenient notation that works.

    It is a way to model what's going on...

  • 0 in reply to manojk peradka
    Guru 227245 points

    manojk peradka said:
    ......but what is the proof behind taking reactances as imaginary

    Not proof: model. Imagine (no pun intended) real numbers on x axis. Any number that strays from the x axis is not real but imaginary (hence the name). It has a real component (along the x axis) and an imaginary component (along the y axis). The vector that points from the origin to teh number has an angel. 0 degrees for real numbers, other than 0 degrees for imaginary numbers.
    Now the phase shift between voltage and current  on a periodic waveform (else it makes no sense talking about a phase shift) can also been shown as an angle on a two-dimensional chart. Zero degrees for pures resistance, other than zero degrees for any impedance with a reactive part. The geometrical representation is the same as for imaginary numbers, hence the math to be used on both is the same.

    Well, "same math for same geometrical representation" could count for a mathematical proof :)

  • 0 in reply to manojk peradka
    Expert 1480 points

    Hello,

    if  you calculate RLC Networks in the time domain, you will get very complicated differential equations which are not that easy to handle.

    One way to make things simple is to transform the equations into another domain, make the calculations, and transform it back to the time domain. This has the advantage, that the calculations are a lot more simple in the other domain than in the time domain. 

    The transformation used in RLC networks is the so called laplace transformation:

    http://en.wikipedia.org/wiki/Laplace_transform

    This transformation transforms from time domain to frequency domain (and back). For example : Capacitor

    Regards Marco

  • 0 in reply to Marco
    Intellectual 300 points

    hello sir,

    thanx for the proof.....even i was thinking of the same today n worked for hours......even i got the same proof.......but i substituted "s" as jw..........even i dont know exactly that how "s" becomes jw.......sir if dont mind may u pls tell me how this relation came..........

  • 0 in reply to manojk peradka
    Guru 227245 points

    manojk peradka said:
    i dont know exactly that how "s" becomes jw

    That's the Laplace transformation that transforms from time domain to Laplace domain and back.

    However, Laplace transformation isn't an easy thing and nothing that could be done 'automatically' by an MSP.
    Usually, you use Laplace to transform your set of time-domain equations not Laplace domain, then solve the equations and the final equation is then transformed back into time domain. In Lpalace domain, epanding, shorting etc. your formulae is much easier than in time domain. The resulting forumula, which still contains your variables, is then de-logarithmized and the final formula is calculated in realtime.

    This method is comparable to using logarithmic transformation so your * turns into a + and your exp simplifies to *. And (most conveniently) / and SQRT turn into - and /.

  • 0 in reply to manojk peradka
    Mastermind 7395 points

    The Laplace transform works on the complex plane number, for any number in the form of s = v + jw. v is the real part of the s complex number, and w is the imaginary part. It can be shown for many systems that to analyze the behavior in "permanent regime" (as opposed to transient regime), it is enough to analyze what happens for the imaginary part of the argument of the funcion. The imaginary part is v=0 => s = jw.

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