Electronics tutorial: basics and Ohm's law

This is the first post about a series of mini basic-electronics tutorials I intend to write. Many of my friends, some engineers, some not, are starting to play around with Arduinos and other microcontrollers; and although they are doing quite well with the programming part, they still struggle to understand why you have to connect everything to ground, what a pull-up resistor is or how Pulse Width Modulation (PWM) works. But first we have to start with the basics.

In this post I am going to talk about voltage, current, resistors and Ohm's law.

Plumbing circuit analogy

I have found water pipes helps me a lot to understand what is going on inside my electrical circuits. I started using this analogy at college, and still use it today when people ask me to explain to them in simple terms how some circuits work.

Even without being a plumber, we all have a basic intuition of how water circuits work, what happens when you have a lot of pressure inside a pipe and how the flow rate changes with the position of a valve. So before we head into electronics, let us talk about water pipes.

Imagine you have a closed water circuits formed by a big loop of pipes filled up with water. As you see, no water can enter nor exit the loop, thus the amount of water stays constant. But you will have also noticed that this circuit is useless, as water will stay still inside the pipes without anything to push them around.

Now imagine we add a pump to the circuit. At the beginning when we turn the pump on the water will slowly start moving in the loop, and because the pipes are very wide the water will gain more and more velocity without need for the pump to push hard.

But if we substitute one of the wide ones with a really narrow pipe the pump will have to push really hard to get the water flowing in the loop, and despite all the effort, the water will not flow as fast as in the previous scenario.


Electronic circuit

The three following figures are the equivalents to the three plumbing examples. You will notice a small triangle on the bottom on all three images, it represents the ground or zero voltage potential. For now you can safely ignore it, I will explain what it is used for in a separate post.

In the first circuit we have a loop of wires. Wires are usually made of copper and due to metallic bonding at atomic level are full of free-moving electrons (so to speak). Electrons have to travel through them just like water does inside pipes, they cannot jump from one wire to another unless there is an electrical connection, and they cannot flow into dead-ends. That means that electrical circuits have to form loops, however, the facts that there are electrons and loops do not imply that electricity exists.

For "electricity" to exist, or more correctly, current, electrons have to move, and that requires a power source that pushes them forward. A voltage source, like a battery, has two poles. On one pole the voltage source pushes electrons out, and on the other pole sinks the returning electrons in, in practice quite similar to how a water pump works.

If you connect the two poles of a voltage source with a wire, which has a negligible resistance, the current or flow rate of electrons can get extremely high because there is nothing that tries to stop them. In that case we are talking about a short-circuit, scenario where the immense current heats up the circuit due to Joule's effect until it break. We will talk about Joule's effect later, but for now you can think of it as a heat-up due to friction inside the wires due to moving electrons.

Finally, if we add a resistor to the circuit we obtain a steady current determined by how hard the voltage source pushes electrons forward, and the magnitude of the resistance. Higher resistances will offer more opposition to the movement of electrons. As we suspect, voltage, current and resistance are tied together by a formula: Ohm's law.

Brief definitions


  • Formal definition: Voltage, electric potential difference, electric pressure or electric tension (denoted ∆V or ∆U) is the difference in electric potential energy between two points per unit electric charge (wikipedia).
  • Informal definition: The difference of how hard the electrons push against each other on two different points of the circuit.  For example, the voltage of a voltage source is measured as the "pressure" (potential difference) between its two poles. Measuring voltage at a single point of the circuit is not possible, as for current to exist electrons have to move from a high potential area to a less potential area (if the potential is equal everywhere, why should they move in the first place? (refer to the first circuit)). However, if we measure at a single point it is because we implicitly assume that its with respect to another point called ground, which we label as a zero potential point.


An electric current is a flow of electric charge. In electric circuits this charge is often carried by moving electrons in a wire (wikipedia).

Current is measured as the charge that pass through a section of wire per unit of time in Amperes [A], which is 1 Coulomb [Q] every second. And one Q are roughly 6.241509 × 10¹⁸ electrons. And therefore, 1A means that every second 6.241509 × 10¹⁸ electrons flow through a wire.


The electrical resistance of an electrical conductor is the opposition to the passage of an electric current through that conductor. (wikipedia).

Resistance is measured in Ohms [Ω], and the bigger its magnitude, the harder it tries to stop passing electrons.

Ohm's law

  • For a given resistance you have to increase the applied voltage to increase the current.
  • If you want to maintain a constant current, you have to increase the resistance if the voltage increases.
  • For a constant voltage, you have to reduce the resistance to increase the current.

All three statements talk about Ohm's law, which can be written as: V = I · R

As you can infer from Ohm's law, if we short-circuit a voltage source, we have R = 0, where I = V/R, thus I → ∞. Also, if we have an infinite resistance which lets no electrons through, current is evidently zero. That is why electrons have to travel through wires, because air as ideally an infinite resistance (its actual resistance is 2 × 10¹⁶ Ω·m).

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