Electrical Circuits: Understanding Key Concepts and Laws
Item 54: Electrical Circuits
Introduction
A circuit or electrical grid is a set of elements combined so that the possibility exists that an electrical current will flow. Depending on the nature of the excitation sources, we obtain several interesting chapters in the study of electrical circuits. If the circuits are time-invariant, they are excited by direct current (DC). If the excitations are sinusoidal functions of time, the circuits are excited by sinusoidal alternating current (AC). The latter is of great practical importance in that sinusoidal alternating current is the basis of systems of generation, transmission, and utilization of electrical energy in large quantities.
Variables of Circuits: Sign Conventions
The main variables involved in the study of electrical circuits are current, voltage, and power.
Electricity: This name is given to the displacement of electric charge along a conductor. Electricity is a phenomenon resulting from the property that all bodies have to be electrically neutralized. Thus, a body whose atoms are negatively electrified tends to yield an excess of electrons, while a body whose atoms are positively electrified tends to be neutralized by taking electrons from other atoms that are in excess. This displacement of electrons is the source of electrical energy or electricity. The current sense of the electrons is from – to +.
Voltage (Potential Difference): It is represented by the letter U. For there to be an orderly movement of charges, i.e., electric current, there must be a source or generator that sends loads, providing energy to put them in motion. The difference of potential (DDP) or voltage between two points on a circuit is the work done in moving the unit charge between those two points.
Electrical Power: Power is work done per unit of time. P = V x I. Electric power is the product of the voltage and the current intensity. The power unit is the watt (W), which is widely used. In mechanics, the unit of power is horsepower (hp), where 1 hp = 736 W. The power loss of a conductor, by circulating an electric current, is a power loss that is the product of the resistance of the conductor by the square of the current intensity: P = R x I2.
Kirchhoff’s Laws
Kirchhoff’s Current Law (KCL): This law is a direct result of the principle of conservation of charge at a node. Consider any circuit, as shown in Fig. 6, in which the reference current directions in different branches are appreciated. Since charges cannot be stored at any instant of time in a node, the total current entering the node must equal the total current coming out of it. Thus, in the node of the figure, it is true that: I1 + I3 + I5 = I2 + I4. In general, the law states: At any instant, the algebraic sum of all currents entering a node equals zero. In the above definition, the term “algebraic” means that the currents have a + sign for incoming flows to the node and a – sign for those leaving.
Kirchhoff’s Voltage Law (KVL): This law is a direct consequence of the principle of conservation of energy. Its statement is as follows: At any instant, the algebraic sum of all voltages around a closed path is zero, i.e., u(t) = 0. In the above definition, the word “algebraic” means that the voltages have signs assigned when you look down the road in a concrete sense: the + sign to the voltage drops and the – sign to the rises, or the reverse. In the circuit of Fig. 6, we take + for voltage drops and – for voltage rises, and the sense of travel is indicated by the arrow. The implementation of this law results in -U1 – U2 + U3 + U4 – U5 = 0.
Coulomb’s Law
The force with which two electric charges attract or repel each other is directly proportional to the product of their charges and inversely proportional to the square of the distance that separates them.
Electrical Resistance
Electrical resistance (R) is the difficulty a material presents to the flow of current. The unit of resistance is the ohm and is defined as the resistance to the passage of electrical current of a column of mercury 106.3 cm long and 1 mm2 in cross-section.
Resistivity
Resistivity is the value of the resistance of a cylinder of a substance with a 1 mm2 cross-section and 1 m in length. It is represented by the letter ρ. The most commonly used values are 0.028 for aluminum and 0.017 for copper.
Resistance of a Conductor
As we said before, the resistance of a conductor also depends on its length (the greater the length, the greater the resistance) and its cross-section (the smaller the cross-section, the greater the resistance). R = ρ x L / S. The resistance also varies with the outside temperature because the values are made at 20ºC. Rt = R0 x (1 + α x Δt)
Current Strength
Current strength (I) is the amount of electricity that flows through a conductor in a unit of time. It is measured with an ammeter. The unit of electric current is the ampere (A).
Ohm’s Law
Ohm’s Law states that “The intensity of electrical current flowing through a conductor is directly proportional to the applied potential difference and inversely proportional to the resistance of it.” It can be expressed mathematically in the following equation: I = V / R. This law is not fulfilled, for example, when the resistance of the conductor varies with temperature, and the temperature of the conductor depends on the current intensity and the time it is circulating. The law defines a specific property of certain materials, laying the ratio: V = I x R. A conductor satisfies Ohm’s law only if the V-I curve is linear, i.e., if R is independent of V and I. (Draw an electronic circuit).
Alternating Current (AC)
Alternating current (AC) is an electric current that changes periodically. The most used AC is that which makes a cycle with sine values. (Draw a wave, alternating positive side, indicating the period up and negative)
Period: The minimum time it takes for the current to repeat its values. In that time, it makes a cycle.
Frequency: The number of cycles in 1 second. Frequency (f) is the inverse of the period (f = 1/T).
Alternation: When the AC flows, it performs two alternations, one positive (+) and one negative (-).
Phase Difference Between Alternating Quantities:
- a) It is said that they are in phase when their maximum and minimum values occur at the same moment.
- b) They have a phase difference of an angle or time T when their maximum and minimum values are outdated by an angle or a time. (Draw 2 cases).
Direct Current (DC)
Direct current (DC) is the continuous flow of electrons through a conductor between two points of distinct potential. Unlike alternating current, in DC, electric charges always move in the same direction (i.e., terminals with higher and lower potential are always the same). Although direct current is commonly identified with constant current (e.g., supplied by a battery), it is continuous as long as it always keeps the same polarity. (Draw a wave of DC).