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Electric current
Electric current
Electric conduction in metals
In metals, the only particles carrying electricity are free
electrons or conduction electrons.
Free electrons
‒ move continuously in a chaotic manner (thermal agitation)
‒ If a potential difference is applied between the ends of a
conductor, a drift velocity is superimposed on the thermal
agitation
If there is a potential difference between
the ends of a conductor, an electric field is
present within its interior, oriented
longitudinally and with the lines of the
field roughly following the profile of the
conductor.
Electric current
Electric current and its direction
An electric current is an orderly movement of particles
carrying electric charge. In metallic conductors the
charged particles that move are the electrons, which
have a negative charge.
‒ the electrons move
from lower potential
towards higher
potential
‒ conventionally, the
direction of the
current is the
opposite
Electric current
If the end A of a conductor has a greater potential than end B, the conduction electrons move
from B to A, while the conventional direction of the current is the opposite: from A to B.
The intensity of electric current
The intensity of electric current flowing in a conductor
is the ratio between the amount of electrical charge Dq
flowing through a cross section of the conductor in a time
interval Dt, and the time interval itself:
The intensity of current in a wire
conductor is the amount of charge that
the electrons carry through a cross
section of the wire per unit of time.
Electric current
Electrical resistance
Electrical resistance
The electrical resistance R of a conductor, at fixed
voltage DV between its ends, is the ratio of DV and the
intensity of the current running through it:
In SI the unit of resistance is the ohm (W)
Electric current
Ohm’s first law
At a fixed temperature, the voltage DV between the ends of
a metallic conductor is directly proportional to the intensity of
the current that runs through it. One therefore has:
where the coefficient of resistance
of the conductor R is constant with
changing DV.
Characteristic curve of a ohmic conductor
Electric current
Resistors
Resistors
have non-negligible
resistance
obey Ohm’s first
law
The symbol with which a resistor is represented in diagrams of
electrical circuits. Often to indicate the resistor we use the
term “resistance”.
Electric current
Electrical circuits
An electrical
circuit
is a path through
which electrical
charges can flow
consists of
various elements
battery
resistors
switches
Open electrical circuit
Electric current
Closed electrical circuit
connecting
wires
Ohm’s second law
At a fixed temperature, the resistance R of a wire
conductor is directly proportional to the length I of the
wire and inversely proportional to the area A of its
cross section. Therefore one has:
where the coefficient of proportionality r depends on
the nature of the material of which the wire is made
r (W  m) is termed the resistivity or specific
resistance of the material
Electric current
Electromotive force
Electric generators
An electric generator maintain a constant current in a circuit
A battery
‒ is an electric generator
‒ connected with two
electrical wires turns
on the light bulb
Electric current
Electric generators and hydraulic pumps
A hydraulic pump
‒ maintains the
difference in height
between the
communicating
vessels.
A generator
‒ maintains the
electrical potential
difference.
Electric current
Electromotive force
The electromotive force (e.m.f.) f of a generator,
equal to the electrical potential difference between its
poles with the circuit open, is the ratio of the work L
carried out to take a positive charge q from the
negative pole to the positive one and the charge itself:
Electric current
Generators and batteries
negative pole
positive pole
Generator
Several generators
connected in series
constitute a
Battery
In a battery the positive pole of
one generator is connected to the
negative pole of the other
Electric current
Direct current (D.C.) electrical circuits
Analyzing a complex D.C. electrical circuit
A current that always flows in the same direction with a
constant intensity over time is called a direct current.
To analyze an electrical circuit
two theorems are applied,
formulated by G. Kirchhoff
Nodal theorem
Mesh theorem
Electric current
Nodal and mesh analysis
Nodal theorem
The sum of the intensities of the currents that arrive at
the node of a circuit is equal to the sum of the intensities
of the currents that are moving away.
Electric current
Nodal and mesh analysis
Mesh theorem
Algebraically summing the potential VA of a point A in the
circuit to all the variations that the potential undergoes in
a circuit of any mesh, we obtain again the value of VA.
In a mesh the algebraic sum of the
potential changes is always nil
Electric current
Resistors in series
Configurations of a complex circuit are always combinations
of two types of links between resistors
in series
Resistors in series connected with a generator.
Electric current
in parallel
Equivalent resistance when linked in series
The set of two or more resistors in series is equivalent to a
single resistance Req such that:
Req = R1 + R2 + R3 + …
Electric current
Resistors in parallel
Resistors in parallel connected with a generator.
A and B are nodes of the circuit
‒ between their ends there is
the same voltage
Electric current
Resistors in parallel
With more than two resistors:
Electric current
Electrical measuring instruments
Measuring
instruments
Voltmeter
Ammeter
Electric current
measures the intensity
of an electric current
measures the
potential difference
must be inserted in series
in the branch to measure
must be inserted in
parallel to the branch
Electrical power
Power of an electric generator
A generator that maintains a direct current of intensity i in
a circuit and a voltage of DV between its poles produces
an output P equal to the product of DV and i:
If the generator has a negligible internal resistance:
Electric current
Joule’s law
The Joule effect is the heating of conductors caused by a
flow of current.
The power PJ absorbed by an ohmic conductor because
of the Joule effect is equal to the product between the
resistance R and the square of the intensity of the current i
PJ is also called “power loss”
Electric current
Measurement of power
The power dissipated PJ is expressed
‒ in watt (SI)
‒ In kilowatt hour
‒ 1 kWh = 3.6 · 106 J
The Joule effect may be
‒ unwanted
‒ useful
‒ electric heaters
For the resistors of electric heaters conductors with high values of resistivity are used.
Electric current