Power in electrokinetic
Fondamental : Definition of power in receptor convention
The electrical power received by the dipole (in receptor convention) is :
The energy received during the time interval is such that :
Fondamental : Conductor and Joule's efficient
For an ohmic conductor :
The electric power received by the conductor is then dissipated as heat to the outside (principle electric heaters).
Fondamental : Average power in forced sinusoidal
The voltage across the dipole (AB) can be written :
And intensity :
Where is the phase shift of the intensity with respect to the voltage.
The instantaneous power received by the dipole AB is (in receptor convention) :
Let (with ) :
And is a sinusoidal function of angular frequency and therefore of period .
The average power is calculated :
The term is called "power factor" : it depends on the impedance of the dipole AB.
Special cases of dipoles :
For resistance :
For perfect coil :
For a capacitor :
In a series circuit (RLC) :
It's well verified that the power is entirely dissipated in the resistor.
For a complex impedance dipole :
Only the real part of the impedance (necessarily positive) involved.
For admittance complex dipole :
Only the real part of the admittance (necessarily positive) involved.
Fondamental : Importance of power factor
The power factor is the term .
If the tension imposed, RMS current required to achieve a given power in a dipole is :
It will be all the weaker as the power factor is close to .
Or decrease the intensity reduces losses by Joule effect in the wires, from generators to the users circuits ; hence the importance to only supply high power factor circuit (usually, ).
Complément : Adaptation of impedances
A stereo system (generator) is connected to the speakers (complex impedance ).
How to choose the speaker impedance for the power received by them to be maximum ?
In this case, we say that there is adaptation of impedance.
We denote :
The average power received by the user dipole is :
How to maximize , with , and fixed (characteristics of the generator) ?
Have been shown and were necessarily positive, while and may be a priori (capacitive circuit) or (inductive circuit). So :
is then chosen to minimize the denominator of .
Expression of power becomes :
It will be maximum if :
The impedances are then complex conjugate :
There is talk of adaptation of impedance.
The maximum power is equal to :