Thread: Electrical impedance

hello guys,

recently when i was reading ahead on my next years physics's course, i saw the term Electrical impedance. now i get the definition and all that general implications towards it, but what i fail to understand is the usage of complex numbers to describe the impedance.

can anyone explain this to me??

thank you.

Originally Posted by Heinsbergrelatz

hello guys,

recently when i was reading ahead on my next years physics's course, i saw the term Electrical impedance. now i get the definition and all that general implications towards it, but what i fail to understand is the usage of complex numbers to describe the impedance.

can anyone explain this to me??

thank you.

Purely resistive electrical circuits are described by algebraic equations that obey Kirchoff's two circuit laws.

RLC (reisitance, capacitance, inductance) electrical circuits are described by ordinary differential equations with constant coefficients.

If you write down the differential equations that describe the circuit and then take either the Fourier transform or Laplace transform of everything in sight you get a set of algebraic equations that look just like the algebraic equations that describe resistive circuits, with the added feature of usiing complex numbers. The complex numbers that describe the dynamics of capacitors and inductors are called "impedance" and are a complex analog of resistance. It makes steady-state circuit analysis of AC circuits easy.

For simple circuits driven by sinusoids there is a messy way to develop this theory without using Fourier or Laplace transforms, but it really obscures what is going on and when you lean about transforms things become a lot more clear.

In a circuit with reactive elements (capacitors and inductors) the voltage and the current do not change in lock step -- they are "out-of-phase" with each other -- so one needs two values to describe them. (This is true in non-reactive Direct Current circuits as well, but the second value is always 0 so it's easy to ignore).

Complex numbers are a convenient way to represent systems that have 2-degrees of freedom -- having two variables. Usually in electronics the real component is thought to be on the X-axis and the imaginary component (the one with the "i" or "j") on the Y-axis. The added feature is that all the usual calculations, when done with complex arithmetic, automagically produce the correct results.

Illiterate slobs can handle this stuff too. At a given frequency, the total impedance of an RC or RL series circuit is the resultant of a quadrature summation of reactance and resistance components. The only out-of-phase condition in an RLC circuit is between the reactances that reduce to positive (inductive) or negative (capacitive) net reactance that forms a perpendicular vector with the resistive component.