Fundamentals of Electrical Quantities

1. Electric Charge: The Foundation of Electricity

Everything in electronics begins with charge. It's a fundamental property of matter, just like mass. To understand charge, we need to look at the structure of an atom.

For a great visual introduction to the atom and the concept of charge, please start by watching the first part of this video.

As the video explained, we can summarize the key points about charge:

• Source of Charge: At the atomic level, charge comes from protons (positive charge, $+e$) and electrons (negative charge, $-e$). Neutrons have no charge.
• Interaction: Like charges repel each other, and opposite charges attract. This force is what allows us to do useful things with electricity.
• Symbol and Unit: Electric charge is denoted by the symbol $Q$ or $q$. Its SI unit is the Coulomb (C).
• Elementary Charge: The smallest amount of charge observed in nature is the charge of a single proton or electron, known as the elementary charge, $e$. Its value is approximately $1.602\times 10^{-19}$ Coulombs. This means one Coulomb is the total charge of about $6.24\times 10^{18}$ electrons.
• Conservation of Charge: Charge cannot be created or destroyed, only transferred from one object to another. This is a fundamental law of physics.

2. Electric Current: The Flow of Charge

Now that we understand charge, the next concept is current. If you have a collection of mobile charges (like the free electrons in a copper wire) and you apply a force to make them move in a particular direction, you create an electric current.

Electric current is the rate of flow of electric charge.

Imagine a river. The flow of water (liters per second passing a point) is analogous to electric current (Coulombs per second passing a point).

Mathematically, if a total charge $\Delta Q$ flows past a point in a time interval $\Delta t$, the average current $I_{avg}$ is:
$I_{avg}=\frac{\Delta Q}{\Delta t}$

Since you are studying calculus, we can express the instantaneous current, $i(t)$, more precisely as the derivative of charge with respect to time:
$i(t)=\frac{dq(t)}{dt}$
This is the most general and powerful definition of current.

• Symbol and Unit: Current is denoted by the symbol $I$ or $i$. Its SI unit is the Ampere (A). One Ampere is defined as the flow of one Coulomb of charge per second (1 A = 1 C/s).

Conventional Current vs. Electron Flow

A crucial point to understand is the direction of current.

• Electron Flow: In metal conductors like wires, the charge carriers that actually move are electrons, which are negatively charged. They move from a point of negative potential to a point of positive potential.
• Conventional Current: However, by a historical convention established long before the electron was discovered, engineers and scientists define the direction of current as the direction that positive charge would flow. This means conventional current flows from a point of higher potential (positive) to a point of lower potential (negative).

In this course, and in all of circuit analysis, we will always use conventional current. The direction of current is indicated by an arrow on circuit diagrams.

3. Voltage: The "Push" Behind the Current

What causes charge to move and create a current? The answer is voltage.

Voltage is the work done or energy required to move a unit of charge between two points. It's the "electrical pressure" or "push" that drives the current.

To build a strong intuition for voltage, please watch the next segment of the video we started earlier. It uses a great analogy involving gravity.

As the video explained, voltage is also called potential difference because it measures the difference in electrical potential energy between two points. A voltage does not exist at a single point; it is always measured between two points.

Mathematically, if it takes an amount of work $W$ (or a change in energy $\Delta U$) to move a charge $Q$ from point A to point B, the voltage $V$ between A and B is:
$V=\frac{W}{Q}\text{or}V=\frac{\Delta U}{Q}$
Again, using calculus, the instantaneous voltage $v(t)$ can be defined as the rate of change of work with respect to charge:
$v(t)=\frac{dw}{dq}$

• Symbol and Unit: Voltage is denoted by the symbol $V$ or $v$. Its SI unit is the Volt (V). One Volt is defined as the potential difference that requires one Joule of energy to move one Coulomb of charge (1 V = 1 J/C).

4. Power: The Rate of Energy Transfer

Finally, let's discuss power. In any physical system, power is the rate at which energy is being used, or the rate at which work is being done.

In an electric circuit, power is the rate at which electrical energy is converted into another form (like heat, light, or motion) or supplied to the circuit.

The mathematical definition of power is the derivative of work (or energy) with respect to time:
$p(t)=\frac{dw(t)}{dt}$

We can find a more direct formula for electrical power by combining the definitions of voltage and current. Using the chain rule from calculus, which you will cover in your studies, we can write:
$p(t)=\frac{dw}{dt}=\frac{dw}{dq}\cdot \frac{dq}{dt}$
We just defined $v(t)=\frac{dw}{dq}$ and $i(t)=\frac{dq}{dt}$. Substituting these in gives us the fundamental equation for electric power:
$p(t)=v(t)\cdot i(t)$
So, the power being consumed or supplied by a circuit element at any instant is simply the product of the voltage across it and the current flowing through it.

For a final clarification on this and the derivation, please watch this last short clip.

• Symbol and Unit: Power is denoted by the symbol $P$ or $p$. Its SI unit is the Watt (W). One Watt is defined as the consumption or supply of one Joule of energy per second (1 W = 1 J/s).

Lesson Summary

We've covered the four most fundamental quantities in electricity. For a quick reference, the article below provides a good text-based summary of everything we've discussed.

Here's a summary table of the key concepts:

Conclusion

In this lesson, you learned to define charge, current, voltage, and power. You now understand that current is the movement of charge, voltage is the force that causes this movement, and power is the rate at which this process consumes or produces energy. The relationships $i=dq/dt$, $v=dw/dq$, and $p=vi$ are fundamental to everything that follows.

In our next lesson, we will introduce our first circuit component, the resistor, and our first circuit law, Ohm's Law. This will allow us to take these abstract concepts and apply them to a simple, practical circuit to calculate exactly how voltage, current, and resistance are related.