Circuit Analysis Part 1: Electric Charge, Voltage, Current, and Resistance
A good place to begin with circuit analysis is to define electric charge, voltage, current, and resistance. This article will discuss basic atomic theory and the charged particles within atoms that produce electrical phenomena, introduce conductors, semiconductors, and insulators, and show how Ohm’s law is used in basic direct current circuit analysis
Electrical Charge
Electrical charge is an intrinsic property of matter that manifests itself in the form of attracting and repelling forces. In atomic theory we know that every atom consists of a nucleus containing positively charged protons surrounded by negatively charged electrons. This force of attraction, where unlike charges are attracted to each other, keeps electrons in orbit around the nucleus.
The force between charges can be modeled with Coulomb’s Law where Q is the charge on an electron, k is a proportionality constant known as the Coulomb’s Law constant that is dependent on the medium that the charged particles are immersed in. In the case of air, k = 9.0x10⁹ Nm²/C². R equals the distance between the centers of the two charges.
In a copper atom, a nucleus containing 29 protons is surrounded by 29 electrons in spherical orbits called shells, identified by the letters K, L, M, and N. The single electron in the N shell is called a valence electron and directly affects the electrical properties of copper.
Atoms normally have an equal number of protons and electrons, so the positive and negative charges cancel each other, leaving the atom electrically neutral. However, the valence electron of cooper is weakly attracted to the nucleus and electrostatic force can easily cause this electron to be ejected from the nucleus’ orbit. This free electron eventually finds a new copper atom and carries its negative charge to the new atom. This chain effect causes a flow of electrons called current.
The Unit of Electrical Charge: The Coulomb
The International System of Units (SI) unit of electrical charge (denoted by Q) is the Coulomb (SI symbol C). The Coulomb is defined as the charge carried by 6.24 x 10¹⁸ electrons. In circuit analysis we are usually interested in the charge moving through a conductor. Therefore when 6.24 x 10¹⁸ electrons move through a wire, we say that 1C of charge has passed through the wire.
Free Electrons
As mentioned above, electric current is produced by the movement of free electrons through a substance. The amount of energy required for electrons to escape their parent atoms depends on the number of electrons in the valence shell. This property directly influences the conductive ability of a substance. Since very little energy is required to free the single valence electron in a copper atom, copper makes an excellent conductor of electricity.
Conductors, Semiconductors, and Insulators
Conductors are materials through which charges move easily. The most common examples are metals such as copper, aluminum, silver and gold, which each have their own characteristics that make them suitable for particular applications. Copper is most widely used because it is inexpensive. Aluminum, while less conductive than copper, is used in overhead power lines because of its light weight. Gold, while expensive, is used in certain critical applications because of its resistance to corrosion.
Semiconductors have half-filled valence shells. Semiconductors like silicon, can be made to act as a conductor or insulator through a process called doping. Silicon is widely used in electronic components like diodes, transistors, and integrated circuits.
Insulators are materials through which charges do not move easily. Common examples are glass, ceramic, plastic, rubber, and wood. Insulators do not conduct charge because they have full, or nearly full valence shells. However it is important to note, that when a voltage of sufficient magnitude is applied to an insulator, its valence electrons can still be torn from their shell and charge will move through the material.
Voltage
Voltage is the potential energy of an electrical source. Voltage can be thought of as the force that pushes electrons through a circuit. Voltage difference between any two points is known as the potential difference (also known as voltage drop). Potential difference is measured in volts (V). Since voltage is the force that pushes electrons through a circuit, it is sometimes referred to as energy or electromotive force (EMF).
Electric Current
Electric Current is the rate of movement (rate of flow) of charge. In the circuit diagram below, current moves from the negative terminal of the battery, through the light bulb (the load), to the positive battery terminal:
Electric current is measured in Amperes (A), where one ampere is the flow of one Coulomb of charge per second.
Batteries as a Direct Current Source
Batteries (the invention of which is credited to Alessandro Volta) are the most common source of direct current (constant voltage source). Batteries produce voltage as a result of a chemical reaction between conductive electrodes and an electrolyte. Many batteries are groups of cells connected together internally. The lead-acid car battery, for example, is often a collection of six 2 volt cells connected together for a total of 12 volts. Batteries can be identified by the following symbols:
Direction of Current
At one time early in the study of electricity, it was believed that current flowed from positive to negative. This is referred to as conventional current direction. Eventually it was discovered that the opposite is true: current, which is the movement of negatively charged electrons, moves from negative to positive. This direction is referred to as electron flow direction. It is important to note that circuit analysis can be done utilizing both directions. However the conventional direction is often taught because of its wide use in industry.
Resistance
Resistance (R) is the natural tendency of materials to resist the flow of charge and is measured in Ohms (represented by the greek letter omega). Resistors with known values are used in circuit design to control the flow of current to other components, lest the components be destroyed by too much current. When current flows through a resistor, a certain amount of the electromotive force or voltage is dissipated in the form of heat. This dissipation through heat is responsible for the voltage drop across a resistor.
Ohm’s Law and the Relationship between Voltage, Current, and Resistance
There exists a relationship between voltage (here represented as E), current (I), and resistance (R) that is defined by Ohm’ Law (discovered by Georg Ohm)with the following equation. The equation can be manipulated to solve for any of the three variables:
Georg Ohm found that at a constant temperature, the electrical current through a fixed resistance is directly proportional to the voltage applied across it, and inversely proportional to the resistance.
Basic Direct Current (DC) Circuit Analysis
Ohm’s law used to find the current (the arrow denotes conventional direction) in the DC circuit below:
Ohm’s law used to find the resistance in a DC circuit:
Ohm’s law used to find voltage supplied by the source in a DC circuit:
Summary
- Electric charge, and as a result, current is produced by valence electrons moving from atom to atom within a substance.
- Conductors have a low resistance value while insulators have a high resistance value. This is due to their number of valence electrons; conductors have few valence electrons while insulators have many valence electrons.
- Voltage is the measure of potential energy between two points in a circuit. Also known as voltage drop.
- Current is caused by the flow of electrons through a circuit.
- Current flow is directly proportional to voltage but inversely proportional to resistance; as voltage increases, current increases but as resistance increases, current decreases.
- Batteries produce direct current.
- Direct current moves in one direction.
- There are two models of current flow: conventional current direction, where current flows from positive to negative, and the electron flow direction, where current flows from negative to positive.
- Even though conventional current direction is technically incorrect, it doesn’t matter in regards to circuit analysis and is most often used in professional and academic circles.
- Resistance is the opposition to current flow.
- Resistors are used to control the current flow to other electronic components.
- Resistors dissipate voltage in the form of heat, producing a voltage drop across the resistor.
- Ohm’s law describes the relationship between voltage, current, and resistance.
- The equation for Ohm’s Law E = I x R, can be arranged to solve for any of the three variables: E = I x R, I = E/R, or R = E/I.
In the next article we will take a deep dive into resistance and discuss resistivity, temperature effects on resistance, types of resistors and their identification, and conductance.
