Friday, April 6, 2018

Why is electrical reactance the imaginary part of electrical impedance?


This is by definition really.


(The real part or x axis  is resistance which dissipates energy by friction etc).


This subject may seem complicated.


Reading mathematics on complex numbers or 2 dimensional vectors helps.


Common sense helps.


Simple experiments with capacitors and inductors, springs and masses, bottles (volume of air) and bottle necks (inertance, or mass of air?) help. A bottle is a resonant circuit and it can produce a tone when we blow to it. Use extreme caution when experimenting especially with big coils or inductors. The risk of a fatal electric shock is great. Inductors try to keep the electron current through them constant. If the circuit is cut suddenly they will react to the change generating extremely high voltage across them for a short time. Just like a car. It has high mass and wants to keep its speed constant. If anything tries to change its kinetic condition great forces are created for a short time and we know how dangerous they are. If for example a car while running even with engine off hits a tree there is irreversible damage to both.


The reactance of inductance, capacitance, mass, compliance is on the imaginary axis or y axis of the 2 dimensional or complex number plane because these elements do not desipate energy but store it and give it back.


They are on the imaginary axis as there is 90 degrees phase difference between excitation and result.


Try oscillating a door back and forth and this will be felt. It is the mass that reacts to the change in velocity that we try to impose. We can feel the phase difference between the force we apply and velocity. See how these qualities change with time as you excite the door sinusoidally.


The voltage across an inductor is proportional to the rate of change of current through it.
V=L times di/dt
The constant of proportionality is the inductance of L


The force by a mass reacting is proportional to the rate of change of its velocity (acceleration).
F=m times du/dt (try oscillating a door back and forth at various excitation frequencies to feel this).
The constant of proportionality is mass or m.
This is the Neuton's law.


The inductor law is the law of induction.


Mass tries to keeps speed constant. (It reacts to change in velocity, observe how the mass of your body behaves while traveling in the bus or metro train while standing up). Inductance tries to keep electric current constant. They behave similarly in nature. And they are governed by similar laws or differential relations or equations.


More than a century ago the study of mechanical or acoustical systems started being systematically analysed by the study of equivalent behaving electrical circuits. Ie circuits with electrical resistance, capacitance inductance.


This was a great aid to the development of microphones such as the Shure Unidyne, which led to SM57, SM58. The great design and development of full range speakers. Moving magnet or moving coil record playing cartridges. The ribbon microphone that Amy Winehouse for example uses to sing Back to Black.


One of the great pioneers and inventors is Harry Olson, director of RCA acoustical laboratory.


References:


Dynamical Analogies - Olson


Introduction to System Dynamics - Shearer, Murphy, Richardson


Engineering Circuit Analysis - Hayt, Kemmerly


Electromagnetism - Grant, Philips


Electricity and Magnetism - Purcell - Berkeley Physics Course


The Feynann Lectures in Physics - Feynmann, Leighton, Sands


A treatise on Electromagnetism - Maxwell


Microphones - Robertson - BBC


Elements of Acoustical Engineering - Harry F. Olson


Conceptual Physics - Hewitt


See the moment Amy Winehouse recorded Back to Black - YouTube


RCA 77DX ribbon microphone - www.coutant.org
























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