Ohm’s Law defines the fundamental association among voltage, current, and resistance within an electrical or electronic circuit.
Basics of DC Circuit Theory
Fundamental DC circuit theory examines the interconnection of electrical elements within an electric circuit. Electric current, which is the flow of charge measured in amperes (A), moves around a closed circuit propelled by a potential difference, known as voltage and measured in volts (V).
All materials are composed of atoms, each containing protons, neutrons, and electrons. Protons carry a positive electrical charge, neutrons are neutral, and electrons have a negative electrical charge. Atoms are held together by strong forces of attraction between the nucleus and the electrons in their outer shell.
While protons, neutrons, and electrons are stable when together within an atom, separating them induces a potential difference, creating an attraction. In a closed circuit, loose electrons move and drift back to the protons due to their mutual attraction, resulting in the flow of electrons, known as electrical current. However, the material through which electrons move imposes a restriction on their flow, termed resistance.
All basic electrical or electronic circuits encompass three interconnected electrical quantities: Voltage (V), Current (I), and Resistance (Ω).
In the realm of DC circuit theory, voltage (V) represents the potential energy stored in an electrical supply in the form of an electrical charge. This voltage acts as a force propelling electrons through a conductor, with a higher voltage having a greater ability to push electrons through a given circuit.
Since energy has the capacity to perform work, this potential energy can be quantified as the work measured in joules required to move electrons, forming an electrical current, from one point or node to another within a circuit.
The disparity in voltage between any two points, connections, or junctions (referred to as nodes) in a circuit is termed Potential Difference (p.d.), commonly known as Voltage Drop. This potential difference, measured in volts with the circuit symbol V or lowercase “v,” signifies the pressure or pushing force, directly correlating with the capacity to perform work.
A consistent and unchanging voltage source over time is termed a DC Voltage, while a source with varying amplitude periodically is referred to as an AC voltage. Regardless of being AC or DC, voltage is measured in volts, defined as the electrical pressure required to force an electrical current of one ampere through a resistance of one Ohm.
Although voltages are typically expressed in volts, prefixes such as microvolts (μV = 10^-6 V), millivolts (mV = 10^-3 V), or kilovolts (kV = 10^3 V) are used to denote sub-multiples of the voltage present. Notably, voltage can have either positive or negative amplitude.
D.C. voltage sources, like batteries, power supplies, or solar cells, provide a fixed-value and polarity direct current. For instance, 5V, 12V, -9V, etc. On the other hand, A.C. voltage sources, such as those powering homes, offices, and industrial applications, have values associated with the supplied power. The voltage and frequency of mains alternating current (AC) electricity commonly used in homes are typically 230 volts AC (230V) in the United Kingdom and 110 volts AC (110V) in the USA.
General electronic circuits function on low-voltage DC battery supplies ranging from 1.5V to 24V DC. The circuit symbol for a constant voltage source typically features a battery symbol with positive (+) and negative (-) signs indicating polarity. Conversely, the circuit symbol for an alternating voltage source is represented by a circle with a sine wave inside.
An analogy can be drawn between a water tank and a voltage supply to illustrate a straightforward correlation. Similar to how the pressure of water increases with the height of the tank above the outlet, the potential energy in a voltage supply rises with higher voltage, leading to the release of more electrons.
Voltage is consistently gauged as the disparity between two points within a circuit, commonly termed the “Voltage drop.” It’s important to note that voltage can be present across a circuit without current, whereas current necessitates voltage. Therefore, any voltage source, whether DC or AC, prefers an open or semi-open circuit condition but is adverse to a short circuit, as it has the potential to cause damage.
In the realm of DC circuit theory, electrical current (I) represents the movement or flow of electrical charge and is quantified in Amperes, symbolized by ‘i’ for intensity. It denotes the continuous and uniform drift of electrons (the negative particles of an atom) throughout a circuit, compelled by the voltage source. In practice, electrons move from the negative (-ve) terminal to the positive (+ve) terminal of the supply. However, for simplicity in circuit comprehension, conventional current flow assumes that the current moves from the positive to the negative terminal.
In circuit diagrams, the current flow is typically indicated by an arrow associated with the symbol ‘I’ or lowercase ‘i’ to denote the actual direction of the current flow. It’s crucial to note that this arrow generally represents the direction of conventional current flow, not necessarily the direction of the actual flow.
Conventional Current Flow
Traditionally, conventional current flow refers to the movement of positive charge around a circuit, going from positive to negative. The illustration on the left depicts the motion of positive charges (holes) within a closed circuit, starting from the positive terminal of the battery, traversing the circuit, and ultimately returning to the negative terminal. This direction of current flow, from positive to negative, is commonly known as conventional current flow.
This convention was established during the early exploration of electricity when it was believed that electric current flowed in a circuit in this direction. In alignment with this convention, arrows in circuit diagrams and schematics, particularly those associated with components like diodes and transistors, indicate the direction of conventional current flow.
Consequently, Conventional Current Flow describes the flow of electrical current from positive to negative, contrasting with the actual flow of electrons, which moves in the opposite direction.
The movement of electrons within a circuit is contrary to the direction of conventional current flow, going from negative to positive. The actual current in an electrical circuit consists of electrons that travel from the negative pole (cathode) of the battery and return to the positive pole (anode).
This occurs because electrons carry a negative charge and are naturally attracted to the positive terminal. This flow of electrons is termed Electron Current Flow, where electrons move around a circuit from the negative terminal to the positive.
Many textbooks utilize both conventional current flow and electron flow. In practice, the direction of current flow, whether using conventional or electron flow, does not impact the actions of current within the circuit. However, conventional current flow, positive to negative, is commonly employed for its simplicity and ease of understanding.
In electronic circuits, a current source is a component providing a specified amount of current (e.g., 1A, 5A, or 10 Amps). The circuit symbol for a constant current source is represented by a circle with an arrow inside, indicating its direction.
Current is measured in Amps, and an ampere is defined as the number of electrons or charge (Q in Coulombs) passing a certain point in the circuit in one second (t in Seconds).
Current is typically expressed in Amps, with prefixes such as microamps (μA = 10^-6A) or milliamps (mA = 10^-3A) used. It’s important to note that electrical current can be positive or negative based on its direction of flow within the circuit.
Direct Current (DC) flows in a single direction, while Alternating Current (AC) alternates back and forth. Regardless of the type, current flows through a circuit only when connected to a voltage source, its “flow” is constrained by both the circuit’s resistance and the pushing force of the voltage source.
Alternating currents and voltages, being periodic and time-varying, have an “effective” or “RMS” (Root Mean Squared) value denoted as Irms, equivalent to the average power loss of a DC current Iaverage. Unlike voltage sources, current sources favor short or closed-circuit conditions and disfavor open-circuit conditions as they impede current flow.
Drawing an analogy to a tank of water, the current is akin to the flow of water through a pipe, with the flow being consistent throughout. Faster water flow correlates with greater current. Notably, current cannot exist without voltage, so any current source, whether DC or AC, favors a short or semi-short circuit but opposes an open circuit as it prevents the flow.
DC Circuit Theory of Resistance
Resistance (R) is the property of a material to impede or hinder the flow of current, or more precisely, the flow of electric charge within a circuit. The component specifically designed for this purpose is referred to as the “Resistor.”
Resistance is quantified in Ohms, denoted by the Greek symbol (Ω, Omega), with prefixes indicating Kilo-ohms (kΩ = 10^3Ω) and Mega-ohms (MΩ = 10^6Ω). It’s important to note that resistance cannot have a negative value; it is always positive.
DC Circuit Theory for Resistor Symbols
The level of resistance exhibited by a resistor is determined by the ratio of the current flowing through it to the voltage across it. This relationship distinguishes whether the circuit element is a “good conductor” with low resistance or a “poor conductor” with high resistance. Low resistance, such as 1Ω or less, suggests the circuit is an effective conductor, typically made from materials like copper, aluminum, or carbon. Conversely, high resistance, at 1MΩ or more, indicates a circuit with poor conductivity, often composed of insulating materials like glass, porcelain, or plastic.
In contrast, a “semiconductor” such as silicon or germanium possesses resistance that falls between that of a good conductor and a good insulator, hence the term “semiconductor.” These materials are commonly used in the production of diodes and transistors.
Resistance can be linear or non-linear in nature but is never negative. Linear resistance adheres to Ohm’s Law, where the voltage across the resistor is linearly proportional to the current passing through it. Non-linear resistance, however, does not follow Ohm’s Law and exhibits a voltage drop across it that is proportional to some power of the current.
Resistance remains constant and is unaffected by frequency, with the AC impedance of a resistance equating to its DC resistance. It cannot assume negative values. It is essential to distinguish between a resistor, which is an electrical component, and resistance, which represents the slope of the straight line defined by Ohm’s law. Resistance is always positive, never negative.
A resistor is categorized as a passive circuit element, incapable of delivering power or storing energy. Instead, resistors absorb power, manifesting as heat and light. The power in resistance is always positive, irrespective of voltage polarity and current direction.
For very low resistance values, like milli-ohms (mΩ), it may be more convenient to use the reciprocal of resistance (1/R) rather than resistance itself (R). This reciprocal is termed Conductance (G), symbolized as the ability of a conductor or device to conduct electricity. Conductance is denoted by the symbol Siemen (S) and is measured in mhos (ohm spelled backward), represented by an inverted Ohm sign (℧). Power can also be expressed using conductance as p = i²/G = v²G.
The relationship between voltage (v) and current (i) in a circuit with constant resistance (R) yields a linear i-v relationship with a slope equal to the value of the resistance.
DC Circuit Theory Summary
By now, you should have gained an understanding of DC circuit theory and the interconnected nature of electrical voltage, current, and resistance. The foundation of this relationship is encapsulated in Ohm’s Law. In a linear circuit with a fixed resistance, an increase in voltage leads to an increase in current, and conversely, a decrease in voltage results in a decrease in current. Simply put, higher voltage corresponds to higher current, and lower voltage corresponds to lower current.
Similarly, altering the resistance in a circuit affects the current flow. An increase in resistance leads to a decrease in current for a given voltage, while a decrease in resistance results in an increase in current. In essence, higher resistance corresponds to lower current, and lower resistance corresponds to higher current.
Thus, the flow of current around a circuit is directly proportional to voltage (V↑ causes I↑) but inversely proportional to resistance (R↑ causes I↓).
Here’s a basic summary of the three units:
- Voltage, or potential difference, measures the potential energy between two points in a circuit, often referred to as its “volt drop.” When a voltage source is connected to a closed-loop circuit, it induces a current flow.
- DC voltage sources use symbols like +ve (positive) and −ve (negative) to indicate polarity. Voltage is measured in Volts, denoted by the symbol V or E for electrical energy.
- Current flow involves both electron flow and hole flow in a circuit. It represents the continuous and uniform movement of charge around the circuit, measured in Amperes (A) with the symbol I. Current is directly proportional to voltage (I ∝ V).
- The effective (RMS) value of an alternating current equates to the average power loss equivalent to a direct current flowing through a resistive element.
- Resistance is the opposition to current flow in a circuit. Low resistance values imply a conductor, while high values suggest an insulator. Current is inversely proportional to resistance (I 1/∝ R).
- Resistance is measured in Ohms (Ω), represented by the Greek symbol Ω or the letter R.
|Unit of Measure
|V or E
In the upcoming tutorial on DC Circuit Theory, we will delve into Ohms Law—an essential mathematical equation elucidating the correlation among Voltage, Current, and Resistance in electrical circuits. This law stands as the cornerstone of electronics and electrical engineering and is precisely defined by the equation: V = I*R.