Circuit Analysis: Mesh, Node Laws, and Passive Elements

Mesh Law

The principle of conservation of energy is applied to circuits through the Mesh Law. Connect a series circuit of three resistors and check that the sum of voltages (measured in each) coincides with the voltage at the terminals from the source. The algebraic sum of all potential differences over a closed path (mesh) in the circuit is zero. That is, Σ ΔV = 0 for a closed course. This theorem is simply a particular way of stating the Principle of Conservation of Energy in electrical circuits, which can be explained from the potential difference defined in terms of work and energy.

Node Law

The principle of conservation of electric charge is expressed through the Node Law. A node is a point where the circuit is divided into branches, but can be considered a node at any point where at least one conductor arrives and at least one departs. In any node, the algebraic sum of the currents must be zero. This theorem, also known as KCL, is simply the statement of the principle of conservation of charge (I₁ - I₂ - I₃ = 0).

Passive Element Characteristics

The characteristic of an element is given by the intensity function f(tension) for the same. To get the same element, it is subjected to various voltage values, and the recorded intensities traversing it are used to build the table of values V/I, which is then graphed.

Diode

A diode is a semiconductor that allows the passage of electric current in one direction, with characteristics similar to a switch. In simple terms, the characteristic curve of a diode (IV) consists of two regions: below a certain potential difference, it behaves like an open circuit (not conducting), and above it, as a closed circuit with very small electrical resistance.

Resistor

A resistor is an electronic component designed to introduce a specific electrical resistance between two points in a circuit. In other cases, such as plates, heaters, etc., resistors are used to produce heat by exploiting the Joule effect. Technicians often use the term resistor to mean more resistance.

Ohm's Law

The intensity of electric current passing through a conductor in a circuit is directly proportional to the voltage applied to its ends and inversely proportional to the resistance of the conductor. Mathematically, this law is expressed as follows: I = V/R, so V = IR, where:

• V is the voltage applied to the ends of the conductor (in volts, V)
• R is the resistance of the conductor (in ohms, Ω)
• I is the amount of current flowing through the conductor (in amperes, A)

Solving for the resistance from the mathematical expression of Ohm's law, we have: R = V/I. Based on Ohm's law, the unit of electrical resistance is defined as follows: the resistance of a conductor is 1 ohm if a current of one ampere flows when a potential difference of one volt is maintained across the resistance. R (in ohms) = V (in volts) / I (in amperes), that is, 1Ω = V/A.

Note that the law has some limitations:

1. It can be applied to metals but not to coal or materials used in transistors.
2. When using this law, remember that the resistance changes with temperature, as all materials are heated by the passage of current.
3. Some alloys are better conductors in one direction than another.