Fundamentals of Electric Circuits: Phenomena, Laws, and Concepts
ITEM 54: Introduction to Electric Circuits
1. Introduction
An electric circuit is the path followed by the movement of electricity. There are three fundamental elements in an electrical circuit:
- The generator (source of electricity)
- The receiver (consumer of electricity)
- Conductors (connect the generator and receiver, allowing the flow of electricity)
When electricity moves along a circuit, various phenomena occur. Understanding these phenomena requires considering electrical quantities and units.
2. Phenomena in Electric Circuits
The passage of electric current through a conductor produces several noticeable phenomena, especially when a sufficient potential difference is maintained for a period of time and the current is intense enough. These phenomena include:
a) Magnetic Effects
Oersted’s Experiment: When a wire carrying an electric current (I) is placed above a compass needle, the needle deflects, indicating the presence of a magnetic field produced by the current.
Rowland’s Experiment: Two annular conductors (C1 and C2) connected to a generator (S) and carrying charges of opposite signs demonstrate the magnetic field produced by a convection current (the movement of charged bodies).
b) Thermal Effects
Joule Effect: A conductor carrying an electric current heats up due to the collisions between moving charged particles and the particles of the conductive medium.
c) Chemical Effects
Electrolysis: Passing an electric current through two platinum wires immersed in a cupric chloride (Cu2Cl2) solution causes chemical decomposition. Alternating current is not suitable for electrolysis.
d) Lighting Effects
This phenomenon occurs when an electric current flows through a gas, such as neon. It can also be observed in electric arcs, where the temperature of a conductor rises due to the Joule effect.
e) Biological Effects
The passage of electric current through a living organism can cause burns, coagulation, and electrocution, with severity depending on the current intensity. These effects are primarily caused by the Joule effect and chemical reactions.
3. Key Electrical Concepts and Quantities
Difference of Electric Potential or Voltage
The potential difference (Vb – Va) is the negative value of work done per unit charge by the electric field when a positive test charge moves from point a to point b. The unit of potential difference is the volt (V), and it is measured using a voltmeter.
Electric Current
Electric current is the amount of electricity flowing through a circuit per unit time (typically per second). The unit of electric current is the ampere (A), defined as the current carrying one coulomb of charge per second. Current intensity is measured using an ammeter.
Electromotive Force (EMF)
Electromotive force (emf) is the force that maintains the movement of electrons in a circuit. It is primarily associated with generators and is measured in volts. Every generator has internal resistance, so the emf only equals the measured voltage across its terminals when the circuit is open (no current flowing).
Electrical Resistance
a) Resistivity
Resistivity (ρ) is the resistance of a cylinder of a substance with a cross-sectional area of one square millimeter and a length of one meter.
b) Resistance of a Conductor
The resistance (R) of a conductor depends on the material it’s made of, its length (L in meters), and its cross-sectional area (S in square millimeters). The unit of resistance is the ohm (Ω). R = ρ x L / S.
c) Conductance
Conductance (G) is the inverse of resistance: G = 1/R.
d) Influence of Temperature on Resistance
The resistance of a conductor generally increases with temperature. This increase is usually linear and is characterized by the temperature coefficient (α).
e) Value of Resistance at a Given Temperature
Knowing the temperature coefficient (α) and the resistance at a reference temperature (e.g., 20°C), the resistance at any other temperature (t) can be calculated: R = R20 (1 + α(t-20)).
Capacitance
Capacitance (C) is the ability of a system of two conductors separated by an insulator to store electrical charge. It is defined as the ratio of the stored charge (Q) to the potential difference (V) between the conductors: C = Q / V. The unit of capacitance is the farad (F), which represents the capacitance of a capacitor that stores one coulomb of charge when the potential difference between its plates is one volt. Capacitance depends on the surface area of the plates, the thickness of the dielectric material, and the dielectric constant of the material.
Electric Power
The power (P) absorbed by a portion of a circuit between points a and b is given by P = I x Vab, where I is the current and Vab is the voltage difference. Power is expressed in watts (W) when I is in amperes and V is in volts.
Electric Energy
To determine the work (W) done by a device, we need to know the power (P) and the time (t) during which it operates: W = P x t = V x I x t.
Sinusoidal Current Intensity
A sinusoidal current is an alternating current whose intensity (i) varies with time according to the equation: i = Im x sin(ωt ± φ), where Im is the maximum current, ωt is the angular frequency, and φ is the phase angle.
Sinusoidal Voltage
Similar to current, voltage can also be sinusoidal, following the same principles.
Period and Frequency
The period (T) of an alternating current is the time it takes for the current to complete one full cycle (return to the same value and direction). It is measured in seconds. Frequency (f) is the number of cycles per second, measured in hertz (Hz). In Spain, the standard AC frequency is 50 Hz. Period and frequency are inversely related: f = 1 / T.
Effective Values of Voltage and Current in AC Circuits
Since voltage and current in AC circuits are constantly changing, it’s useful to define their effective values. The effective value of current (I) is the equivalent DC current that would produce the same heating effect in a resistor. I = Im / √2. Similarly, the effective value of voltage (V) is calculated using the same formula.
Inductance
Inductance (L) is the ratio of the total magnetic flux created by a current in a coil to the current itself.
Capacitive Reactance
Capacitive reactance (Xc) is the opposition a capacitor offers to the flow of alternating current at a given frequency: Xc = 1 / (ωC).
Inductive Reactance
Inductive reactance (Xl) is the opposition an inductor offers to the flow of alternating current: Xl = ωL.
Impedance
Impedance (Z) is a measure of the total opposition to the flow of alternating current in a circuit containing resistance, inductance, and capacitance in series. Its magnitude is given by |Z| = √(R² + (ωL – 1/(ωC))²). In complex form, impedance is represented as Z = R + jX = R + j(ωL – 1/(ωC)), where R is the resistance and X is the reactance.
Admittance
Admittance (Y) is the inverse of impedance: Y = 1 / Z = G + jB, where G is the conductance and B is the susceptance.
4. Fundamental Laws of Electric Circuits
Ohm’s Law
a) General Principle
If two points with a potential difference are connected by a conductor, an electric current will flow through the conductor. Two conditions are necessary for current flow: a potential difference and a continuous electrical circuit connecting the two points.
b) Ohm’s Law Equation
The current (I) flowing through a conductor is directly proportional to the voltage (V) applied across it and inversely proportional to its resistance (R): I = V / R.
Joule’s Law
The interaction of electric current with the atoms of a conductor causes heating. The heat generated is proportional to the square of the current, the resistance of the conductor, and the time the current flows.
Kirchhoff’s Laws
is necessary to define the following concepts: Node. This name is given to any point where they meet over two conductores.Rama. It received its name any portion of the circuit between two neighboring nodes cualesquiera.Malla or closed circuit. The set of branches that can be covered so that any part of a knot, you come back to it, provided that no passing is twice for the same node or branch.b) Kirchoff’s first law: In all knot of drivers the sum of the currents that come to him equals the sum of the currents coming out of it. c) Kirchoff’s Second Law: In any circuit closed or mesh currents, the difference of all time and counterclockwise emf is exactly equal to the difference in voltage drops time and counterclockwise.