Electricity is the flow of electric charges through a conductor, a fundamental phenomenon that underlies modern electrical engineering. This movement of charges follows well-established physical principles, which have been systematically formulated into a set of fundamental electrical laws.
These basic laws of electrical engineering, developed over centuries by pioneering scientists, govern the behavior of electric fields, currents, and circuits. Understanding these electrical laws is crucial for designing and analyzing electrical systems, from simple circuits to complex power networks.
The most important laws related to electrical energy are:
Coulomb's law
Coulomb's law states that the electric force between two charged objects is inversely proportional to the square of the distance between them and directly proportional to the product of their charges. This force acts along the line joining the two charges and can be either attractive or repulsive depending on the nature of the charges.
The law, introduced in 1785 by the physicist Charles-Augustin de Coulomb, is essential in understanding electrostatic interactions in physics and engineering, playing a crucial role in fields such as electronics and electrochemistry.
Formula
where:
- F is the electrostatic force,
- q₁ and q₂ are the magnitudes of the charges,
- r is the distance between the charges,
- k is Coulomb's constant.
Ampere's law
Ampere's law was developed by the Frenchman André-Marie Ampère in 1831. Ampere's law relates a static magnetic field to its cause. It was later corrected by James Clerk Maxwell and became part of Maxwell's equations.
Ampere's law indicates that the circulation of the magnetic field intensity in a closed contour is proportional to the electric current that flows in that contour.
Formula
where:
- B is the magnetic field,
- dl is the differential length element,
- μ₀ is the permeability of free space,
- I_enc is the enclosed current.
Ohm's law
Ohm's law states that the intensity of electric current flowing through a conductor connecting two points is directly proportional to the voltage between the two points and inversely proportional to the electrical resistance of the conductor.
Ohm's law describes with great precision the behavior of almost all electrically conductive materials. However, there are some conductive materials that do not follow this law. These are called non-ohmic conductive materials.
The law is named after the German physicist George Ohm. In 1827, George Ohm described the currents and voltages that occurred in simple electrical circuits. In his honour, resistance is expressed in Ohms (Ω).
Formula
where:
- V is the voltage,
- I is the current,
- R is the resistance.
Faraday's law
Faraday's law of electromagnetic induction is a fundamental principle in electromagnetism that explains how a changing magnetic field induces an electric current in a conductor. This law is the foundation for many electrical devices, including:
- Transformers, which transfer electrical energy between circuits through electromagnetic induction.
- Inductors, which store energy in a magnetic field when current flows through them.
- Generators, which convert mechanical energy into electrical energy by moving conductors through a magnetic field.
This law was discovered by Michael Faraday in 1831. Joseph Henry discovered this law before Faraday in an independent study in 1830, but he did not publish this discovery. Therefore, this law is called Faraday's law.
Formula
where:
- ? is the induced electromotive force (emf),
- Φ_B is the magnetic flux,
- t is time.
Kirchhoff's electrical laws
These laws are composed of two fundamental principles that we explain below:
Kirchhoff's current law (node law)
Kirchhoff's current law, also known as the node law , is based on the conservation of electric charge. When we consider a node in an electrical circuit, this is a point where several conductors are connected.
According to this law, the sum of the currents entering a node must equal the sum of the currents leaving that node. In other words, there can be no charge accumulation at the node; charge entering must leave.
This electrical rule is expressed mathematically as follows:
where:
-
The sum of currents entering a node equals the sum of currents leaving it.
This means that if you have several currents flowing into a node, and several currents flowing out of it, the total sum of the currents entering minus the total sum of the currents leaving is equal to zero.
If you add up all the currents coming in and going out, the total must be zero.
Kirchhoff's stress law (mesh law)
Kirchhoff's voltage law, or mesh law, is based on the conservation of energy in a circuit.
This electrical law states that if you draw a closed path (or mesh) in a circuit, the sum of all the voltage drops along that path must equal the sum of the voltages (energy sources) in the same path.
Specifically, the law says that:
- When you pass through a component that consumes power (such as a resistor), the voltage drop is counted as negative.
- When you pass through a voltage source (like a battery), the voltage is counted as positive.
So if we add up all the tensions in a closed path, we get zero:
where:
-
The total voltage supplied equals the total voltage drops in a closed loop.
This principle implies that the total energy supplied in the circuit is equal to the energy consumed.
It's like you're traveling along a route: if you start and end at the same place (like on a mesh), the total altitudes (tensions) you go up must equal the total you go down.
Gauss's law
Gauss's Law is a principle in electromagnetism that describes how the electric flux through a closed surface is related to the amount of electric charge within that surface.
In simple terms, this law states that if you imagine a sphere or any closed shape around an electric charge, the total electric flux leaving that surface is directly proportional to the charge that is enclosed within it.
The idea behind this electrical law is that the electric flux represents how many electric field lines pass through the surface. If there is more charge inside the surface, there will be more field lines coming out of it. This principle applies regardless of the shape of the surface, as long as it remains closed.
Formula
where:
- E is the electric field,
- dA is the differential surface element,
- Q_enc is the enclosed charge,
- ε₀ is the permittivity of free space.