# Understanding Fundamentals of Current, Voltage, and Resistance

**Created and Edited by Kenneth (Alex) Jenkins - Fall 2023. Edited by Anshu Dendukuri - Spring 2024**

The central concept in understanding the fundamentals of current, voltage, and resistance is unraveling the essential principles that govern the flow of electric charge. Current represents the rate of this flow, voltage signifies the driving force behind it, and resistance encapsulates the opposition encountered in the circuit. A grasp of these fundamentals is crucial for navigating the intricacies of electrical systems and technology.

## Ohm's Law

Ohm's Law, a fundamental principle in electrical engineering, establishes a foundational relationship between resistance, voltage, and current in a circuit. Named after the German physicist Georg Ohm, the law states that the current passing through a conductor between two points is directly proportional to the voltage across the two points, given a constant temperature. Mathematically expressed as [math]\displaystyle{ {I = \frac{V}{R}} }[/math], where I is the current in amperes, V is the voltage in volts, and R is the resistance in ohms, Ohm's Law is instrumental in unraveling the dynamic interplay between these three essential electrical parameters. This law provides a straightforward framework for understanding how changes in voltage or resistance influence the flow of current, and vice versa. Mastery of Ohm's Law is indispensable in analyzing and designing electrical circuits, serving as a cornerstone for engineers and enthusiasts as they navigate the intricate relationships among resistance, voltage, and current in the realm of electronics.

## Current

Current, in the realm of electrical circuits, refers to the flow of electric charge through a conductor. It is the rate at which electrons move along a closed path, commonly a wire or circuitry. Measured in amperes (A), current is a fundamental concept in understanding the dynamic behavior of electricity. The flow of electrons is driven by the electric potential difference, or voltage, which propels them from areas of higher potential to lower potential. Visualizing current involves picturing the movement of these charged particles, akin to a river of electrons streaming through the conductive pathways of a circuit. Whether in the context of powering household appliances or enabling complex electronic devices, a clear comprehension of current is pivotal for navigating the principles that underpin the functioning of electrical systems. By convention, current is measured in the opposite direction of which electrons flow. This is likely because when current was first discovered, electrons had not yet been established in the scientific world. Hence, it could seem like positive charges were moving in a certain direction, rather than negative ones in the opposite as we know today. This convention still stands to this day, and in fact most likely makes calculations simpler, due to not having to account for the negative sign (-), which could cause for mistakes in calculations. However, it is certainly possible to solve a circuit problem with the opposite direction current, just with everything negated.

## Voltage

Voltage, within the realm of electrical systems, is a measure of electric potential difference between two points in a circuit. It can be thought of as a change in electric potential, meaning that if there is no change, the voltage must be 0. Voltage does NOT measure anything at a given point, which is why a voltmeter must be connected at two different points in order to display a reading. These points should have some sort of change in current between them to be non-zero, such as the existence of a resistor or a node. It represents the force that propels electric charges, typically electrons, to move through a conductor. Measured in volts (V), voltage serves as the driving factor behind the flow of current. It can be likened to the pressure in a water pipe that dictates the movement of water molecules; similarly, voltage dictates the movement of electric charges. Higher voltage implies a greater force pushing the charges, while lower voltage corresponds to a less forceful push. Understanding voltage is pivotal in comprehending the dynamics of electrical circuits, as it influences the rate and direction of the electric current, forming a foundational concept in the broader study of electrical engineering and technology.

## Resistance

Resistance, in the realm of electrical systems, is the property that hinders the flow of electric current. It is a measure of the opposition encountered by the flow of electrons as they traverse through a conductor. This opposition leads to the conversion of electrical energy into heat. Resistance is quantified in ohms (Ω), and it is a critical factor in determining the behavior of circuits. Materials with high resistance impede the flow of current more strongly than those with low resistance. Resistors, specific components designed to introduce resistance intentionally, are commonly employed in circuits to regulate and control the flow of current, demonstrating the essential role that resistance plays in shaping the characteristics and functionality of electrical systems. This is because, when given the choice (such as a node splitting into two), current will try to flow through the wire with less resistance. This is why voltmeters are made with such high resistance - to avoid affecting the current flow (by having current flow through the voltmeter instead of the circuit), such an example why high resistance might be beneficial. A nuanced understanding of resistance is vital for engineers and enthusiasts alike as they design and optimize circuits for various applications.

## Analogy to Water

Circuitry can be conceptually likened to the flow of water through a network of pipes, providing an insightful analogy that simplifies the complex dynamics of electrical systems. In this analogy, electrical circuits serve as the conduits for the flow of electrons, analogous to water molecules coursing through pipes. The fundamental principles governing the behavior of both water and electrical circuits draw intriguing parallels, offering a relatable framework for understanding the intricate world of electronics.

Just as water moves from a source to various destinations through a network of interconnected pipes, electrical circuits facilitate the flow of electric current from a power source to multiple components within a system. The pipes themselves can be equated to conductive materials, such as copper wires, that guide the electrons along a predetermined path. Much like the pressure applied to water influencing its movement through pipes, voltage serves as the driving force behind the flow of electrons in a circuit.

Resistors within an electrical circuit find an analogy in the narrowing of pipes or the introduction of obstacles that impede the smooth passage of water. These resistive elements in a circuit limit the flow of electric current, generating heat in a manner akin to the friction-induced warmth observed in constricted water pipes. Capacitors and inductors, on the other hand, can be compared to the storage tanks and coiled sections in a water system, respectively. Capacitors store electrical energy, analogous to water reservoirs, while inductors store energy in a magnetic field, echoing the potential energy stored in coiled pipes.

The analogy of circuits as conduits for the flow of electrons, similar to water coursing through pipes, serves as a didactic tool, allowing individuals to grasp the intricacies of electrical systems through a familiar and tangible metaphor. Just as plumbing systems distribute water efficiently, electrical circuits enable the controlled movement of electrons, powering a myriad of devices and technologies that have become integral to our modern way of life.

### Examples of the Water/Pipe Analogy

For a demonstration, please consider watching this video produced in collaboration with the EATON company.

The electronics retailer Sparkfun also made a video in similar format to EATON's, covering the topics in a much more in depth way.

## Connectedness to Applications Outside of Physics

The concepts encapsulated in Ohm's Law transcend the confines of physics, resonating profoundly in the realm of engineering and various practical applications. Engineering disciplines, particularly electrical and electronic engineering, heavily rely on the principles outlined in Ohm's Law to design, analyze, and optimize a myriad of systems and devices. Understanding the interplay between resistance, voltage, and current allows engineers to predict and control the behavior of electrical circuits, ensuring the efficient and safe operation of electronic components.

In the field of electrical engineering, Ohm's Law is a cornerstone for designing circuits with specific performance characteristics. Engineers leverage the law to determine the appropriate resistances needed for components, calculate voltage drops across various elements, and establish the current requirements for optimal functionality. Whether designing intricate integrated circuits or power distribution systems, the principles of Ohm's Law provide a fundamental framework for engineers to achieve desired electrical outcomes.

Beyond traditional engineering disciplines, Ohm's Law finds application in diverse technological domains. For instance, in the burgeoning field of renewable energy, such as solar power systems, understanding the relationship between voltage, current, and resistance is crucial for designing efficient energy conversion and storage systems. Similarly, in telecommunications, where signal integrity is paramount, the principles of Ohm's Law guide the design of communication networks, ensuring reliable transmission of information through cables and electronic components.

In essence, the universality of Ohm's Law extends its influence into a spectrum of engineering applications, shaping the way professionals approach challenges in fields ranging from electronics and telecommunications to renewable energy. Its principles serve as a practical and indispensable tool, providing a systematic approach to understanding and manipulating the behavior of electrical systems in the pursuit of technological innovation.

## Initial vs Steady State

A critical difference in steady state vs. initial state circuits is how capacitors behave. Initially they are uncharged, and so charge will flow to them to be stored. At steady state, the capacitor is fully charged and the current there is zero. Therefore, if there is a loop with a capacitor, it can be treated as "open" (essentially as if the wire were not connected there, and loop rules as such would apply.

## History

In the early 19th century, the study of electricity was in its infancy, and it was during this time that German physicist Georg Simon Ohm made groundbreaking contributions, laying the foundation for what would become Ohm's Law. Ohm, born in Erlangen, Bavaria, in 1789, embarked on his scientific journey in an era marked by fervent exploration into the nature of electricity.

Georg Simon Ohm's pioneering work culminated in 1827 when he published his seminal treatise "Die galvanische Kette, mathematisch bearbeitet" ("The Galvanic Circuit Investigated Mathematically"). In this work, Ohm unveiled the relationship between voltage, current, and resistance, providing a mathematical formula that encapsulated the fundamental principles. His revolutionary concept, known today as Ohm's Law, asserted that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to the resistance it offers.

Ohm's Law addressed a pressing need in the scientific community at the time, offering a quantitative framework to comprehend and manipulate electrical circuits. It was a watershed moment that transformed electricity from a mysterious force into a quantifiable and predictable phenomenon.

The practical implications of Ohm's Law began to unfold as the fields of physics and engineering evolved. Michael Faraday's groundbreaking work in electromagnetic induction in the early 19th century and James Clerk Maxwell's formulation of Maxwell's Equations in the mid-19th century further enriched the understanding of electricity, providing context to Ohm's Law.

As electrical science progressed, so did the understanding of voltage, current, and resistance. The introduction of the telegraph in the mid-19th century and the subsequent development of electrical power distribution systems in the late 19th century underscored the practical utility of these concepts. Engineers and scientists across the globe, including luminaries like Thomas Edison and Nikola Tesla, applied the principles elucidated by Ohm to propel the electrical revolution, shaping the modern technological landscape.

In summary, Ohm's Law emerged as a cornerstone in the historical tapestry of electrical science, catalyzing a transformative shift in how electricity was understood and harnessed. Its profound impact resonates through centuries, influencing the trajectory of technological progress and laying the groundwork for the sophisticated electrical systems that define our contemporary world.

## See also

### Further reading

Access to IEEE Xplore (a digital library covering all aspects of Electrical and Computer Engineering) is provided for free through the Georgia Tech Library. The library offers various free ebooks covering topics of Power Systems, and Electricity and Electronics Fundamentals.