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 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 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.

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)

Characteristic curve of a ohmic conductor 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

have non-negligible resistance Resistors have non-negligible resistance obey Ohm’s first law Resistors The symbol with which a resistor is represented in diagrams of electrical circuits. Often to indicate the resistor we use the term “resistance”.

Open electrical circuit Closed electrical circuit Electrical circuits An electrical circuit is a path through which electrical charges can flow consists of various elements battery resistors switches connecting wires Open electrical circuit Closed electrical circuit

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 (  m) is termed the resistivity or specific resistance of the material

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 generators and hydraulic pumps A hydraulic pump maintains the difference in height between the communicating vessels. A generator maintains the electrical potential difference.

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:

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

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

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.

In a mesh the algebraic sum of the potential changes is always nil 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

Resistors in series Configurations of a complex circuit are always combinations of two types of links between resistors in series in parallel Resistors in series connected with a generator.

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 + …

Resistors in parallel A and B are nodes of the circuit Resistors in parallel connected with a generator. A and B are nodes of the circuit between their ends there is the same voltage

Resistors in parallel With more than two resistors:

Measuring instruments Electrical measuring instruments Measuring instruments Ammeter Voltmeter measures the potential difference measures the intensity of an electric current must be inserted in parallel to the branch must be inserted in series in the branch to measure

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:

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 The power PJ absorbed by a circuit is also called “power loss” PJ is also called “power loss”

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.