Chapter 12

# 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 :

Power in receptor convention

## 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 :

Is :

Whence :

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) :

So :

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 :

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 :