Fundamentals of Electricity and Circuit Dynamics and Circuit Theory

The Nature of the Electric State and Charge Carriers

All matter is composed of atoms, which in their fundamental state are electrically neutral. The electric state of an object is determined by the gain or loss of electrons from these neutral atoms. If a neutral atom loses one or more electrons, it becomes a positively charged ion. Conversely, if a neutral atom gains electrons, it becomes a negatively charged ion. In general physics, we observe that any body in an electrical state (possessing a net charge) exerts a force of attraction on small, lightweight objects.

Electrification can occur through several physical processes. One common method is friction (dörzsölés), where two different materials are rubbed together; during this process, one body becomes positively charged while the other becomes negatively charged. Another method is contact (érintés), where a charged body touches a neutral or differently charged body, causing the second body to acquire the same type of electrical charge as the first. The interaction between these charges follows a fundamental law: like charges (positive-positive or negative-negative) repel each other, while opposite charges (positive-negative) attract each other.

Electric Current and the Conditions for Its Flow

Electric current is strictly defined as the directed, ordered movement of electric charge carriers. In metallic conductors, these charge carriers are typically free electrons, while in electrolytes, they are ions. For a continuous electric current to be maintained within a system, specific conditions must be met. First, a closed circuit must be established to provide a continuous path for the charges. Second, an electric source (such as a battery or generator) must be present to provide the necessary energy. Third, the circuit must consist of conducting materials that allow for the free movement of charges.

Electric Voltage and the Mechanism of Electrical Work

Electric voltage, denoted by the symbol $U$ , is a physical quantity that describes the work performed by the electric field as it moves a unit of charge from one point to another within a circuit. This relationship is fundamentally tied to mechanical work. When a charge moves within an electric field, we can calculate the work ( $W$ ) using the formula $W = U \times Q$ , where $Q$ represents the amount of charge. Consequently, voltage can be expressed as the ratio of work to charge:

$U = \frac{W}{Q}$

The standard unit for measuring electric voltage is the Volt, represented by the symbol $V$ . The voltage provided by a source is essentially the potential difference that drives the flow of current through the connected components.

Electric Current Intensity

Electric current intensity, or simply current, is denoted by the symbol $I$ . It is defined as a quantity that characterizes the rate of flow of electric charge through a specific cross-section of a conductor. Specifically, it represents the amount of charge ( $Q$ ) passing through the cross-section per unit of time ( $t$ ). The mathematical expression for current intensity is:

$I = \frac{Q}{t}$

The SI unit for current intensity is the Ampere, denoted by the symbol $A$ . If a high number of charges pass through the conductor in a short period, the current intensity is high; if fewer charges pass or if they move slower, the intensity is lower.

Electrical Resistance and its Physical Causes

Electrical resistance, denoted by the symbol $R$ , is a measure of the opposition that a material offers to the flow of an electric current. Its unit of measurement is the Ohm, represented by the Greek letter $\text{Ω}$ . On a microscopic level, resistance occurs because the moving charge carriers (such as free electrons) frequently collide with the stationary atoms or ions that make up the crystal lattice of the conductor. These collisions hinder the free flow of electrons, effectively "slowing" them down and converting some of the electrical energy into heat.

In practical circuit analysis, we also consider internal resistance ( $R_b$ ), which refers to the inherent resistance found within the electric source itself. Every conducting component, including the wires and the power source, contributes some level of resistance to the overall circuit.

Ohm's Law for a Section of a Circuit

Named after the physicist George Simon Ohm, Ohm's Law establishes a direct proportional relationship between the voltage across a conductor and the current flowing through it, provided the physical conditions (like temperature) remain constant. For a specific section of a circuit, the law is written as:

$U = I \times R$

This formula allows us to calculate any of the three variables if the other two are known. It demonstrates that for a fixed resistance, increasing the voltage will lead to a proportional increase in current. Conversely, for a fixed voltage, increasing the resistance will result in a decrease in the current intensity.

Circuit States: Open Circuits and Short Circuits

A circuit can exist in different operational states that determine whether or not current can flow. An open circuit (szakadás) occurs when there is a break in the conducting path, such as an open switch or a broken wire. In this state, the resistance becomes effectively infinite, and the electric current cannot reach its destination, meaning no current flows ( $I = 0$ ).

A short circuit (rövidzárlat), denoted in some contexts as $I_{sc}$ (short-circuit current), occurs when the two poles of an electric source are connected directly with a conductor of negligible resistance, bypassing the intended load. Because the resistance ( $R$ ) is extremely low, the current intensity ( $I$ ) becomes dangerously high according to Ohm's Law. Short circuits are hazardous as they can lead to extreme heat generation, melting of wires, and fire.

Factors Determining the Resistance of a Conductor

The resistance of a specific conductor is not a random value but depends on its physical dimensions, material composition, and environmental factors. The four primary factors are as follows:

Length of the conductor ( $l$ ): Resistance is directly proportional to the length of the wire. A longer wire provides more opportunities for collisions between electrons and the lattice, thus $R \times l$ .
Cross-sectional area ( $A$ ): Resistance is inversely proportional to the cross-sectional area of the wire. A thicker wire (larger area) provides more space for electrons to flow, reducing the frequency of collisions, thus $R \times \frac{1}{A}$ .
Material quality (Resistivity, $\rho$ ): Different materials have different internal structures. The specific resistance or resistivity ( $\rho$ ) is a constant that depends on the type of material (e.g., copper vs. aluminum).
Temperature: The resistance of most metallic conductors depends heavily on their temperature. As temperature increases, the atoms in the crystal lattice vibrate more vigorously, which increases the likelihood of collisions with moving electrons, thereby increasing the electrical resistance.

The comprehensive formula combining the physical dimensions and material properties is:

$R = \rho \times \frac{l}{A}$