Before you start working with circuits, you need to understand the main concepts upon which the core of electrical engineering lies. Understanding the basics will help you keep up with the material and reduce the number of errors you make in the future. While there are some very important equations that you need to know, circuit analysis is not simply a matter of plugging numbers into an equation. You need to understand what voltage, current, and resistance is, and how they relate to each other in order to take advantage of those equations and understand what’s really going on in the circuit. This article will introduce you to the most basic concepts.

### Engineering Notation

In this course and many other courses in the department, we want you to work with engineering notation. Scientific notation is useful for *very* small or *very *large numbers. However, you should use and familiarize yourself with engineering notation for all other numbers. Some common engineering prefixes are shown in the table below.

### Electric Charge

You know that an atom, in its neutral state, has a charge of zero. You also know that if a neutral atom gains an electron, it becomes an ion with a charge of 1-. This definition of charge works fine when talking about one atom, but when working with large numbers of atoms, a more practical definition of charge is needed, i.e. electric charge. The unit for electric charge (denoted by the letter ‘q’) is the Coulomb (C). When measured in Coulombs, an electron has a charge of approximately -1.60 × 10^{−19} C. A proton, then, would have a charge of +1.60 × 10^{−19} C.

*Example:* Find the charge of 5.1×10^{18} ions of copper (Cu). Each copper ion has a charge of 2+.

*Solution:* The copper ions have a surplus of protons, which means that the copper will have a positive charge. Multiply the fundamental charge of each ion times the number of ions. This gives the number of extra protons. Now multiply the number of extra protons by the charge, in Coulombs, of a proton.

**q = 2 x 5.1 x x 1.60x**** = 1.63 C**

### Coulomb’s Law

Coulomb’s law defines the magnitude of the force between two charges as:

where q_{1} and q_{2} are the two charges in Coulombs, r is the distance between the two points in meters, and the permittivity constant of free space is equal to 8.85 × 10^{−12} F/m (Farads/meter). If the force is negative, the two charges attract each other while a positive force means the two charges repel each other. The constant is known as the electrostatic constant Kc, where

Note: Newtons (N) are a unit of force.

If you’ve ever experimented with magnets, then you have witnessed this law before. Two magnets repel and attract each other depending on the orientation of their poles. This equation also shows that the force between two charges grows exponentially as they move together because of the r^{2} in the denominator. You may have noticed this phenomenon as well. Two magnets attract or repel each other when placed very close together, but the force between them dies off rather quickly as they’re pulled apart.

### Electric Current

Current is the flow of charge per unit time and is measured in amperes (A). Current is represented by the letter ‘I’.

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As the formula above indicates, one amp of current is equal to the flow of one Coulomb of charge per one second. In other words, a wire carrying one amp of current moves one Coulomb of charge through the wire every second. When you are working with electricity, keep in mind that one amp is a large amount of current; less than 100 mA of current can kill you!

### Voltage

Voltage is the difference in electric potential between two points and is measured in Volts (V). If you’ve taken physics, electric potential is similar to the concept of potential energy, except in this instance, electric potential is equal to the potential energy per unit charge. Voltage can be seen as the electric pressure, or driving force, that causes current to flow. You may also see voltage referred to as electromotive force.

An important concept to understand when working with voltage and current is that there can be voltage without current flow, but there cannot be current flow without a voltage. For example, think of two people on opposite sides of a box. If both of them apply the same amount of force, the cart will not move. However, if one of them applies more force, the box will move. In both instances, a force (voltage) was applied to the cart (electrons), but only when there was a difference in force did we witness the cart move (current).

### Conventional Current Flow

In the example above, the cart moves away from the person applying more force toward the person applying less force. Current and voltage interact in a similar manner in that current flows from higher voltages to lower voltages. In other words, current is said to flow from the positive terminal of a battery to the negative terminal. This is because current is described as the flow of positive charges. The electrons that actually carry the charge through the wire have a negative charge. Therefore, by definition, current flows in the opposite direction of the flow of electrons.

### Water Analogies

The challenge of learning the concepts of electricity is that electrons are hard to see and it’s hard for people to tell what is going on in a circuit. Analogies to water have been made to help people understand different concepts encountered in electrical engineering. Current, as you might have guessed, is compared to the flow of water while voltage is the difference in water pressure between two points. More water analogies will be made throughout the course to help you understand new concepts.

This water analogy provides another example of how there can be voltage, but no current. Think of the build up of pressure behind a dam. The dam pushes back on the water, allowing no water to flow. This situation is similar to a battery. An ideal 12 V battery always has a potential difference between its terminals of 12 V, but no current flows until the battery is connected to a circuit.

#### Final Remark

Current is a through variable and voltage is an across variable. Current flows through circuits, voltage does not. Rather, voltage is the *potential* for current to flow. When referring to voltage, never say “the voltage through the resistor.” Instead, say “the voltage across the resistor” or “the voltage at a node.” This article was written and edited by Ryan Eatinger, Kansas State University (reatinge@ksu.edu), thanks for the donation.

That covers a lot of introductory concepts! If you have any questions feel free to comment.