Impedance is by definition the ratio of voltage across 2 points to the current that flows through them.
Voltage and current are vectors, so impedance is too.
How come and they are vectors?
When we talk AC, ie vibrations, or oscillations, they not only have magnitude but also phase.
They are complex numbers having a real and an imaginary part.
How come?
AC means sinusoidal oscillation.
Imagine holding in our hand a LED torch.
We then make a perfect circular motion with our hand but we always point the torch perpendicularly to the wall.
We see the light projection creating a perfect sinusoidal oscillating motion on the wall.
The radius of our hand is the amplitude of this motion.
The angular velocity is analogous, proportional to frequency. This is why the angular frequency equals to 2 times PI (3.14...) times frequency. Or ω=2πf.
And the angle our hand makes at any particular moment is the phase.
So, circular motion is a very convinient way to represent vibration, oscillation.
Our hand moves on a plane.
The torch in our hand is at any particular instant at a different 2 dimension point.
The x axis is the real axis. And the y axis is the imaginary axis.
This is why we need complex numbers, ie vectors or numbers of the type (a,b), or a+jb, or e to the power of jωt where t is time or rotating vectors or phasors. They are more or less the same thing.
Impedance also exists of course on mechanical systems, acoustical systems etc.
On mechanical systems it is defined as the ratio of force to velocity.
On acoustical systems as the ratio of pressure to air velocity.
Back to electrical...
Current and voltage may be not be in phase. This happens on capacitors and inductors.
The same on mechanical systems. This happens on masses. And springs. Mass is the analogue to inductance. And springiness is analogous to capacitance. A spring is the analog of a capacitor. The capacitor tries to keep the voltage constant, the scoring tries to keep the force constant.
They obey exactly the same equations.
It is expected since they behave in exactly the same way.
By Newtons 2nd law, mass tries to keep its velocity constant and opposes changes by creating force or vice versa. (It is not easy to accelerate or stop a car).
Same with inductance it tries to keep current through it constant and opposes changes by creating voltage.
This is why an inductor in series cuts treble or high frequencies and an inductor in parallel cuts bass as on Pleiades filters. It has a lower impedance the lower the frequency is and causes a greater voltage drop at the output of a microphone. This is because a microphone has a non zero output impedance usually 200 ohms. So there is an internal voltage drop at the mic due to ohm's law.
On resistance the voltage and current are in phase.
Same on mechanical resistance or friction.
If we oscillate our palm on the beach by rubbing sand we can feel that force and velocity are in phase.
We can also feel that impedance is independent of frequency.
The same with electrical resistance of resistors on an electrical or electronic circuit.
But not so for inductance or capacitance where the reactance, (the imaginary part of impedance depends on frequency).
Why imaginary part?
Because the cause and effect are 90 degrees out of phase.
We can feel this in a very easy way on mechanical systems.
On sand as we said we feel force and velocity in phase.
But not on mass which is the equivalent of inductance.
Try for example holding in your hand something that has mass.
If we oscillate our hand at a low frequency it is easy but it gets progressively difficult the higher the frequency we want to produce.
This is a high cut filter together with the driving output impedance of ourselves.
If we try to do the same to a door which has a much higher mass we further feel this. And we have a high cut -3 dB point (amplitude drop of door oscillation) which happens now at a lower frequency.
This is inductance in series.
Or rather mass.
And we can readily feel that the sinusoidal force we apply and the sinusoidal velocity are not in phase. it may not be 90 degrees as there is friction too or resistance and we have to add vectors!
Analogous things happen with capacitors and springs, and volumes of air of bottles. And necks of bottles.
And when capacitances and inductances are connected we have electrical oscillation. Electrons move back and forth.
Same as when mass and spring are joined where we have mechanical oscillation.
Same as on a bottle. The mass of air in the neck behaves as mass or inductance trying to keep flow constant. The volume of the bottle like a spring or capacitor.
And when we carefully place our ear at the neck of the bottle we can hear the resonant frequency and if we blow we can produce a sustained oscillation.
References:
Introduction to System Dynamics - Shearer, Murphy, Richardson - MIT - Addison Wesley
Music Physics and Engineering - Olson (Staff Vice President Acoustical and Electromechnical Research, RCA)
The Feynman Lectures on Physics - Feynman, Leighton, Sands - Caltec - Addison Wesley
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