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§ 1 The electric current.

The power and current density.

EMF and voltage

I. Any ordered (directed) movement of electrical charges called electric current. When an external electric field E in the conductor starts moving charges, ie generates an electric current. With positive charges move across the field, and negative - against the field. Take over the direction of current direction of movement of the positive charges. For the origin and the existence of an electric current requires two conditions:

1) the presence of free charge carriers (ie the substance must be conductors or semiconductors at high temperatures),

2) The presence of an external electric field.

For a quantitative description of the electric current is introduced - current intensity - scalar physical quantity equal amount of electrical charge transferable per unit time through a cross-section S.

- for direct current, and

- for alternating-current.

Current, which intensity and direction do not change with time, is called permanent.
The current density
 - vector physical quantity that is numerically equal to the force of current flowing through a unit area perpendicular to the current.

- for direct current, and

- for alternating-current .

II.       To a portion of the conductor under consideration is a current I, is necessary to maintain a constant potential difference between these points of the conductor.        к ЭДС    In order to maintain a constant potential difference across the ends of the conductor must be connected to a power source. The current source does work on moving electrical charges along the chain. This work is done by external forces - forces no electrostatic origin, acting on charges of side of the power supply. The nature of external forces may be

different (except fixed charges):
1) chemical reaction - in galvanic cells (batteries), rechargeable batteries,
2) Electromagnetic - in generators. The generator can use a) mechanical energy - hydro, b) nuclear - nuclear reactor) heat - TPS, z) of the tides - PES, D) Wind - Wind Farm, etc.
3) use of the photoelectric effect - photovoltage in calculators and solar powe4) piezoelectric - pezoEDS, such as piezolighter,
5) contact potential - thermopower in thermocouples etc.
The field of external forces, electric charges move inside the power supply against the forces of electrostatic field, whereby the terminal current source and is supported by the potential difference in the circuit current is flowing.

The current source is characterized by an electromotive force – EMF




EMF determined by the work performed by external forces to move a unit of positive charge along the closed circuit.


                        Sided force is equal to :


where  - the field of external forces. The work of external forces on the movement of the charge q on a closed portion of the chain is :

A fs                Efs


ie EMF equal to the circulation of the intensity vector of external forces. At site 1 - 2 (see picture) except of external forces force acting the electrostatic field

ie the resultant force on the section 1 - 2 equals

F net



For a closed circuit


Voltage U on the site 1 -2 called physical quantity determined by the work done by the total field of electrostatic (Coulomb) and external forces when moving a unit positive charge on this part of the chain



§ 2 Ohm's Law

1. Ohm's law for a homogeneous region of the chain.

Called homogeneous area free of EMF.

The current in the homogeneous chain site is directly proportional to the voltage and inversely proportional to the resistance of chain


R 1 Ohm - the resistance of the conductor, which at a voltage of 1 V 1 A current flows.

 G -

electrical conductivity. G (Siemens).

The resistance R of the conductor depends on its size and shape, as well as the conductor material.



where ρ - resistivity of the conductor - the resistance per unit length of the

ℓ - the length of wire; S - cross-sectional area of the conductor.

2. Ohm's law for the inhomogeneous region of the chain

Inhomogeneous called chain section containing EMF.




-- Ohm's Law for the inhomogeneous region of the chain in the integrated form

3. Ohm's law for a closed circuit (full circuit).

wherewhere R - the resistance of the external circuit,
r - the source EMF impedance, then

 -Ohm's law for the complete chain

4. Ohm's law in differential form






σ  -electrical conductivity; sigma


Ohm's law in differential form.

The current density is directly proportional to the electric field E. The coefficient of proportionality σ - electrical conductivity.


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