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
67
0
why we are describing the impedance as a complex quantity and not as a real quantity ?

Apr 5, 2008
19,903
4,138
3. PRS Well-Known Member

Aug 24, 2008
989
36
It makes the math easier.

4. Papabravo Expert

Feb 24, 2006
12,278
2,723
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
67
0
please explain elaborately .

6. Papabravo Expert

Feb 24, 2006
12,278
2,723
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 Thread Starter Active Member

Mar 15, 2009
67
0
Thank you very much !!!!

8. Papabravo Expert

Feb 24, 2006
12,278
2,723
You're welcome

9. KL7AJ AAC Fanatic!

Nov 4, 2008
2,208
427
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 Expert

Feb 24, 2006
12,278
2,723
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 Well-Known Member

Aug 24, 2008
989
36
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.