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Back To Basics Episode 5: Kirchhoff’s Laws – The Rules Of Circuits

Welcome back to Back To Basics, our journey to master electronics one little bit at a time.

So far, we have covered the essentials: safety, basic tools of the trade, and the important Ohm’s law, the foundational relationship between voltage, current, and resistance.


But what happens when circuits get more complex than a single resistor? What about parallel branches, multiple power sources, or a complex resistive network? We need a bigger, better set of rules. Today, we’re introducing the two most powerful, indispensable rules in circuit analysis: Kirchhoff’s Laws.

Named after physicist Gustav Kirchhoff, these laws are the foundation for everything we do next. By the end of this video, you’ll be able to analyze any basic series or parallel circuit and understand how energy and charge are conserved inside the wires.

KCL

Let’s start with the simplest concept, the one you can’t argue with: Kirchhoff’s Current Law, or KCL. KCL is all about the conservation of electric charge. It states that: The algebraic sum of currents entering a node (or junction) must be equal to the algebraic sum of currents leaving that node.


Think of it as a plumbing pipe junction, or a traffic merge lane. If you have 5 Amperes of current flowing into the junction, you must have 5 Amperes flowing out across all the outgoing paths. Charge can’t just pile up or disappear in a wire—it must be conserved. Simply put: What comes in must come out!


We call the meeting point of three or more wires a node. Mathematically, we express this as: The sum of currents entering the node equals the sum of currents leaving the node.


Let’s look at this simple parallel circuit.


We have a total current It leaving the battery. When it hits the first parallel junction (the node), it splits into two branch currents, I1 and I2. KCL immediately tells us that the total current is the sum of the branch currents.


So, It = I1 + I2. And here is the clever part: at the next node, I1 and I2 meet up again to form the original total current It, as it returns to the battery. KCL is your sanity check for all parallel circuits.

KVL


Let’s now talk about the other law, which is about the principle of energy conservation in a circuit: Kirchhoff’s Voltage Law, or KVL.
KVL governs the voltages around a closed loop—any path that starts and ends at the same point.


KVL states that: The algebraic sum of all the voltages around any closed loop in a circuit is equal to zero.


To understand the meaning of this statement, let’s use another analogy. Imagine a roller coaster, which works based on the physics concept of potential energy. The battery (the voltage source) is the lift hill that gives the car potential energy—a voltage rise. The resistors are the dips, loops, and brakes that use up or drop that energy—the voltage drops. When the car returns to the loading platform, its net change in height—its net potential energy—is zero.


In a circuit loop, the energy supplied by the source must be completely dropped across the components. If we trace the entire loop, the sum of voltage rises and drops must be zero.


In this simple series circuit, we have a source voltage (VS) and three resistors with voltage drops V1, V2, and V3 across them. If we trace the loop, always in the same circular direction representing the flow of the current, going from the negative to positive terminal of the battery is a rise, and going across each resistor in the direction of current flow is a drop.


KVL says:
Vs -V1 – V2 – V3 = 0


Rearranging this equation shows us that the source voltage is exactly equal to the sum of the voltage drops:
Vs = V1 + V2 + V3


KVL is the reason why the voltage splits up in a series circuit. The total energy has to be accounted for, and it must balance out to zero when you return to the start. If your KVL equation doesn’t equal zero, you’ve made a mistake!

Circuit Analysis Application


Now for the fun part: let’s put KVL, KCL, and our trusty Ohm’s Law together. This is where you unlock your circuit analysis superpower.


Here is a classic intermediate circuit: a series resistor, followed by two parallel resistors, all connected to a battery. We cannot simplify this down to a single equivalent resistance as easily. So… what do we do?

First, we look at the main node where the total current (IT) splits. KCL immediately gives us our first equation:

It = I2 + I3


Next, we apply KVL to the main loop. We have one voltage rise (Vs) and three drops: across R1, R2, and R3. Wait, we only need to account for the components in the loop.

Let’s apply KVL to the outer path: The source voltage minus the drop across R1 minus the drop across R2 must equal zero.

Vs – VR1 – VR2 = 0


And here’s the trick. We use Ohm’s law, V = IR, to replace the voltage drops with their corresponding currents and resistances.

Since It flows through R1 and I2 flows though R2, our final KVL equation becomes:

Vs – (It * R1) – (I2 * R2) = 0

Now we have two equations,

It = I2 + I3 and

Vs – (It * R1) – (I2 * R2) = 0


and we can create a third for the second inner loop:


Vs – (It * R1) – (I3 * R3) = 0


By substituting and solving this system of linear equations, we can find any unknown current or voltage in the circuit! This is the power of Kirchhoff’s Laws.

Conclusion


Today, we have learned that all complex circuits follow two simple, unbreakable rules: Charge is conserved (KCL), and energy is conserved (KVL). These are the cornerstone principles that every electrical engineer and technician uses daily.


In the next episode of Back To Back, we are going to examine a new component that can be used in electronic circuits: the capacitor. From there, a whole new world will open to us, filled with voltages and currents that change over time and can be used for many, many applications.


Happy experiments!!!

Companion Video:

Back To Basics Episode 2 – The ABC Of Electricity: Voltage, Current & Resistance

Welcome to the second episode of the series “Back to Basics”.

Did you ever wonder what’s actually happening inside a wire when you flip a light switch? What is electricity really?

People knew about electricity since a very long time, but although they observed the related natural phenomena, they didn’t know how to explain them.

They could see a thunderstorm and a lot of lightning, but they didn’t know what lightning was and so they attributed it to angry divinities that used the thunder bolts to punish bad people.

They could stroke a bar made of amber and they would see it attract light pieces of other materials. But they didn’t know why that was happening so they attributed that phenomena to magic.

It was only in the 19th century that humanity finally got a better understanding of electricity. They understood the physical principles behind it and learned how to use it, first for their own pleasure, then for actually do some work to help themselves.

And finally we learned how to use electricity to do the most incredible things: light up our houses, create radios, TVs, computers, robots, and everything you can think of today.

If you would like to understand more about electricity and, maybe one day, be able to bend it to your will, just follow me in this series and its companion videos on YouTube. Through that, you will learn concepts like voltage, current, resistance, capacitance and inductance; and you will learn how the devices around us are made of, and about the electronic components.

And, moving forward, you will learn how to build new things out of those components and, who knows? Maybe one day you will be the great inventor that will revolutionize again our society.

Let’s start today with some basic concepts: voltage and current, and how they are related to each other.

What Are Voltage And Current?

What is voltage? Think of it as of some form of energy that moves things around. The typical example is a river that flows down a hill.

The height of the hill from which the water flows represents the voltage, which is measured from the bottom to the top of the hill. The higher the hill, the higher is the potential energy of the water, and the higher is the voltage. If you’d like to go a little deeper on the concept of voltage, you may want to watch this video:

The current, instead, is made of all the droplets of water that flow down through the river. Such droplets, in terms of electricity, are called electric charges.

The height of the hill is the same as the voltage of a battery, the wire connected to the battery is the bed of the river, and the water that flows in the river is the electric current in the wire.

The higher the hill, the more water will flow down the river. The higher the voltage of the battery, the more electric current will flow in the wire.

For more details on the concept of current, you may want to watch this video:

We measure the voltage in Volt and the current in Ampere. We usually represent these measurement units with the letters V and A. And we can measure these entities with instruments that are called volt-meters and ampere-meters, or am-meters for short, just like we measure the height in meters and the amount of water that flows down the river in liters/second.

Well, yes, in US people is more accustomed with yards and gallons than meters and liters, but you got the point.

In more precise terms, volt is the ratio between the potential energy provided by a battery and the amount of charge needed to generate it.

Current, on the other end, is the amount of charges flowing through a section of the wire in one second.

Back at the beginning of the 19th century, an Italian scientist named Alessandro Volta was conducting experiments on frogs.

He discovered, inadvertently, that touching a dissected leg with two metal sticks made of two different materials, the leg contracted, as if it was still alive. Curious about what happened, he started experimenting with different metals and different watery solutions mimicking the fluids in the frog’s leg. Soon, he discovered a way to generate electricity. He just invented the battery, which he called pile, since it was made of a pile of metal and paper disks, moistened with an acidic solution.

Today, we call that device a voltaic pile, made of several voltaic cells, to honor the inventor of the device that revolutionized our civilization.

After that, other people started experimenting with this newly found source of electricity, and names like Georg Simon Ohm and Andre’-Marie Ampere became famous in that same century. Yes, just about 200 years ago.

What Is Resistance?

In particular, Andre’-Marie Ampere found a way to measure the current flowing in a piece of metal when a voltage was applied to it.

Georg Ohm, instead, used the voltaic pile to run experiments on different kind of materials, to figure out how they behaved when in the presence of a voltage.

He prepared a set of metal bars of different materials and same section, connected each bar to the pile, and measured the amount of current that was flowing through. Then he changed the voltage applied to the bar, by increasing or decreasing the number of cells in the pile.

And with that he discovered that for the same bar, the ratio between voltage and current, whatever the voltage was, never changed. He called this ratio the resistance of the material. And he further discovered that different materials have different resistances.

Ohm’s Law

Today, we have named Ohm the measurement unit of the property he discovered, and we represent it with the Greek letter Omega, which sounds like the initial of the name Ohm.

We write that the Voltage V and the current I are directly proportional as per this formula

where R, the resistance, is the constant of proportionality.

In terms of their measurement units, we also write

This is what we call “Ohm’s Law, which is the foundation for the calculations of voltage and current in any electric and electronic circuit.

As you can see, the three concepts of voltage, current and resistance are not independent; they are all linked together by the fundamental principle called Ohm’s law. On the same resistance, more voltage causes more current to flow. With the same voltage, a higher resistance allows a smaller current to flow. And with the same current, a higher resistance causes a higher voltage.

Conclusion


I hope this helps demystifying the very basic concepts of electricity. In the next episodes we will go deeper into these concepts, we will learn how to measure these entities, we will learn about electronic components, how to use them in circuits, learn how to read schematics, and so forth. Please let me know in the comments what concepts you are more interested in, so I can better aim this series of tutorials to your likes.

Finally, if you like, you can also watch the video version of this post: