Table of Contents
Understanding Basic Electrical Quantities ⚡
In electrical engineering, almost everything you will analyze or design is described using a small set of fundamental quantities. In this chapter you will meet the most important ones: electric charge, electric current, voltage, power, and energy. These are the language of circuits. You will see how they relate to each other through a few simple but very important relationships.
You do not need advanced math here, only comfort with basic arithmetic and the idea of rate, such as "kilometers per hour" or "liters per second." We will build intuition step by step and keep the details of circuits and components for later chapters.
Electric Charge 🧲
Electric charge is the most basic electrical quantity. Matter is made from particles, and some of these particles carry charge. In ordinary materials, the charge carriers are usually electrons, which have a very small quantity of negative charge.
Electric charge is a physical property. Objects can have positive charge, negative charge, or be electrically neutral. At a simple level, you can think of charge as a kind of "electrical stuff" that can move around and produce electrical effects. When charges move, we call that electric current, which we will discuss shortly.
The unit of charge is the coulomb, written as C. One coulomb is a very large amount of charge at the scale of individual electrons. A single electron has a charge of about
$$q_e \approx -1.6 \times 10^{-19}\,\text{C}.$$
This means that one coulomb of charge corresponds to about
$$\frac{1\,\text{C}}{1.6 \times 10^{-19}\,\text{C/electron}} \approx 6.25 \times 10^{18}$$
electrons. Engineers usually do not count individual electrons, but it helps to realize how many are involved when we talk about ordinary electrical currents.
Charge can move from one place to another, but in an isolated system the total amount of charge is conserved. You can transfer charge using friction, contact, or induction, yet the net charge never appears from nowhere or disappears entirely.
Key idea: Electric charge is measured in coulombs (C) and is conserved. It can move and redistribute, but the total charge in an isolated system remains constant.
Electric Current 💧
Electric current describes how fast electric charge flows. If charge moves through a conductor such as a metal wire, we say a current exists in that wire. You can compare this to water flowing in a pipe. The more water that passes a point per second, the larger the water flow rate. For current, instead of water volume per second, it is charge per second.
Formally, the electric current $I$ is defined as the rate of change of charge $Q$ with respect to time $t$. In most beginner circuit analysis we treat this simply as
$$I = \frac{Q}{t}.$$
If 2 coulombs of charge pass through a cross section of a wire in 1 second, then the current is
$$I = \frac{2\,\text{C}}{1\,\text{s}} = 2\,\text{A}.$$
The unit of current is the ampere, written as amp or A. One ampere is one coulomb of charge passing a given point every second:
$$1\,\text{A} = 1\,\frac{\text{C}}{\text{s}}.$$
In circuits you will often see currents much smaller than 1 amp, such as milliamps (mA) which are thousandths of an amp. Even very small currents involve enormous numbers of electrons moving each second.
There are two ideas of current direction. Real electrons in metal wires drift from negative potential to positive potential. However, electrical engineering uses a convention called conventional current, where current direction is taken as the direction positive charge would move, from positive terminal to negative terminal. This convention is used in circuit diagrams and equations, regardless of the actual charge carrier type.
Definition: Electric current $I$ is the rate of flow of electric charge, measured in amperes (A).
$$I = \frac{Q}{t}.$$
Voltage: Electric Potential Difference 🔋
Voltage describes the electrical "push" that drives charge through a circuit. A useful everyday analogy is height in a water system. If water is stored higher up, gravity gives it potential energy per unit volume, and it can flow downwards. Similarly, voltage is related to electrical potential energy per unit charge.
More precisely, if a charge moves between two points in an electric field, the electric potential energy changes. The voltage between those two points is the change in potential energy per unit charge:
$$V = \frac{W}{Q},$$
where $V$ is voltage, $W$ is electrical work or energy in joules (J), and $Q$ is charge in coulombs (C).
The unit of voltage is the volt, written as V. One volt is one joule per coulomb:
$$1\,\text{V} = 1\,\frac{\text{J}}{\text{C}}.$$
If a battery has a voltage of 9 V between its terminals, this means that for each coulomb of charge that moves from the positive terminal through an external circuit to the negative terminal, the electric field does 9 joules of work on that charge.
Voltage is always a difference between two points, not an absolute amount at a single point. That is why you always see it written as, for example, "5 V between point A and ground."
In circuits you might hear voltage called electric potential difference or just potential. The term "voltage source" refers to something that maintains approximately constant potential difference between its two terminals, like an ideal battery.
Definition: Voltage $V$ is electric potential difference, equal to electrical energy per unit charge, measured in volts (V).
$$V = \frac{W}{Q}.$$
Electric Power ⚙️
Power describes how fast energy is transferred, converted, or used. In mechanics you may know that power is "work per unit time." In electricity it is similar. Electrical power tells you how quickly electrical energy is being delivered or consumed.
The basic definition of power is
$$P = \frac{W}{t},$$
where $P$ is power in watts (W), $W$ is energy or work in joules (J), and $t$ is time in seconds (s). One watt is one joule per second:
$$1\,\text{W} = 1\,\frac{\text{J}}{\text{s}}.$$
Electrical power in a circuit element depends on the voltage across it and the current through it. To see this, recall that voltage is energy per unit charge, and current is charge per unit time. If $V$ is the voltage across an element and $I$ is the current through it, then in a time interval $t$ the charge that passes is $Q = I t$, and the energy involved is $W = Q V = I t V$. Substituting into $P = W/t$ gives
$$P = \frac{W}{t} = \frac{I t V}{t} = V I.$$
This relationship is extremely important in electrical engineering.
Core formula: Electrical power is the product of voltage and current.
$$P = V I.$$
This formula lets you quickly determine how much power a device uses if you know the voltage and current. For example, if a small DC motor draws 0.5 A from a 12 V supply, then the electrical power supplied to the motor is
$$P = V I = 12\,\text{V} \cdot 0.5\,\text{A} = 6\,\text{W}.$$
In practical situations, positive power usually means the element is absorbing energy, such as a resistor that heats up or a lamp that lights up. Negative power can indicate the element is supplying energy, such as an ideal source, but sign conventions are discussed more thoroughly in later circuit chapters.
Electrical Energy 🔋➡️🔥
Energy is the capacity to do work. In electrical systems, energy can be stored, transferred, and converted into other forms like heat, light, or motion.
Energy and power are related through time. If power is constant, energy is simply
$$W = P t,$$
where $W$ is energy in joules, $P$ is power in watts, and $t$ is time in seconds.
Using the earlier relation $P = V I$, when voltage and current are constant over time, the electrical energy transferred is
$$W = V I t.$$
This tells you, for example, how much energy a device consumes when it runs for a certain time at a known voltage and current.
Everyday electricity bills often use the unit kilowatt hour which is a unit of energy, not power. One kilowatt hour means 1 kilowatt of power used for 1 hour. Since 1 kW is 1000 W, and 1 hour is 3600 seconds, this is
$$1\,\text{kWh} = 1000\,\text{W} \times 3600\,\text{s} = 3.6 \times 10^6\,\text{J}.$$
So, if a 100 W light bulb is turned on for 10 hours, it uses
$$W = P t = 100\,\text{W} \times 10\,\text{h} = 1000\,\text{Wh} = 1\,\text{kWh}.$$
This is exactly the amount you would be billed for as "1 kilowatt hour" of consumption.
Key relationship: Energy is power multiplied by time. For constant voltage and current,
$$W = P t = V I t.$$
Summary of Core Relationships 📚
It is useful to see the main quantities and relationships in one place. The following table summarizes the definitions introduced in this chapter. Do not worry yet about resistance or more complex circuit behavior. Those topics are covered later. Here the focus is on how the basic electrical quantities fit together.
| Quantity | Symbol | Unit (symbol) | Basic definition | Example formula |
|---|---|---|---|---|
| Charge | $Q$ | coulomb (C) | Basic electrical property of matter | $Q = I t$ |
| Current | $I$ | ampere (A) | Rate of flow of charge | $I = \dfrac{Q}{t}$ |
| Voltage | $V$ | volt (V) | Energy per unit charge | $V = \dfrac{W}{Q}$ |
| Power | $P$ | watt (W) | Rate of energy transfer | $P = \dfrac{W}{t} = V I$ |
| Energy | $W$ | joule (J) or kWh | Ability to do work | $W = P t = V I t$ |
Remember that these formulas describe idealized relationships, but they form the foundation for almost everything you will study in circuits and electrical systems. Later chapters will introduce how resistance, components, and circuit laws link these quantities in real designs.