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 4: Let’s Talk About Resistors

Hi there! Welcome to the fourth episode of Back To Basics, where we explore everything electronics from the beginning.

It is time to start learning about components, and what’s better than beginning with the ubiquitous resistor, a component present in each and every electronic circuit.

We will cover some theory, the math, and the major kind of resistors available on the market. All with a very simple approach that will help you understand what resistors are for, and which one to choose for your own projects and experiments.

Controlling The Flow


Before we get to the components, let’s look at the three ways materials behave electrically.

There are three fundamental kind of materials:

  • conductors,
  • insulators, and
  • resistors

Conductors allow current to flow very easily, like for example in copper wires. They have a high conductivity, which translates in a very low resistance.

Insulators are the opposite of conductors. They block the current flow, like for example with rubber or plastic. They have a very low conductivity, which translates in a very high resistance.

In between these two categories we have the resistors, which are capable of controlling the current flow. They lay in between the conductors and the insulators in terms of conductivity, having very specific values of resistance.

You can view resistance like a water pipe. Conductors are very large water pipes, which offer minimal resistance to the flow of water, here representing the electric current.

Insulators are totally clogged pipes, where the flow of water is totally stopped.

And finally the resistors, which are like water pipe of a specific section, so that they limit the flow of water to specified amounts.

The Fundamental Rule: Ohm’s Law


The math that governs the current flow through a resistor is called Ohm’s Law, and it is the most important concept in electronics.


Here is the formula:

V = I R

where:

V is the voltage, or the entity that forces the current to flow, which is measured in Volt; I is the current, or the flow rate of the charges, which is measured in Ampere; R is the value of the resistance, or the entity that opposes to the flow of current, which is measured in Ohm.

Resistor Calculations: Series And Parallel

Most of the time we need to create circuits with multiple resistances, connected in various ways. Two most common ways of connecting components are the series connection and the parallel connection.In both case, resistors can be replaced with an equivalent resistance.


Here is an example of two resistors, R1 and R2, connected in series. When resistors are connected this way, there is only one path for the current and the equivalent resistance R3 is just the sum of the resistances in series.


And here is an example of two resistors connected in parallel. In such cases, the current splits into multiple paths when it enters the parallel, and it regroups when it leaves the parallel. The equivalent resistance is the reciprocal of the sum of the individual reciprocal resistances.

Note the simplified formula on the right, only valid in the case of only two resistances in parallel.


You can see that when resistors are in series, the total resistance increases, while when the resistors are in parallel, the total resistance is smaller that the smaller resistor in the parallel connection.

Practical Example

Let’s put this information into practice.

Let’s say we have a 9V battery, a resistor, and a LED. Knowing that the current that must flow through the LED is 20mA, and that the voltage at the LED is 2V, what’s value of resistor we have to put in series to the LED to limit the current to the 20mA value?

Since the three components are all in series, the current will be the same through all of them. Since we want a 20mA current through the LED, then also the resistor will be traversed by a current of 20mA. Additionally, the volt at the resistor is given by the difference between the voltage value on the left and the one on the right. The voltage on the left is the battery voltage. The voltage on the right is the voltage required by LED, which is 2V.

Using Ohm’s law, we can therefore write:


So, in practice, if we want to power an LED using a voltage source of 9V, we need to put a resistor in series with a value of 350 Ohm.

Physical Components: Types Of Resistors


Let’s now take a look at the kind of resistors we can find on the market and how they are made.

We have two main categories based on the physical aspect of the resistors:

  • through hole resistors, or THT resistors, usually in the shape of a cylinder with two wires coming out of them, and
  • surface mounted resistors, or SMT (or SMD) resistors, usually in a cubic and small shape.


We can also categorize resistors as fixed or variable. All fixed resistors can be either THT of SMD resistors. The variable resistors can be mechanically variable, thermally variable, or electromagnetically variable.


A typical example of mechanically variable resistors are the potentiometers, which usually have three terminals, the usual two at their two ends, and a third one, connected to a sliding connector touching the resistive material between the two ends. Measuring between one of the two end terminals and the slider, we can obtain all the resistance values between zero and the nominal value of the potentiometer.


Thermally variable resistors are usually called thermistors. They have two leads, and their resistance value changes with the temperature.


An example of electromagnetically variable resistor is the photo-resistor, a resistor that changes its resistance with the intensity of the light.


The resistance value of resistors can be imprinted on the resistor itself in two different ways, depending on the kind of resistor. It can be just printed using only numbers, the last of which always represents the number of zeros following the other numbers. Or it can be printed using numbers and the letter R, which represents the decimal point. Or it can be imprinted in the form of colored bands.


Here are a few of examples of number representations:


And here is an example with numbers with a decimal point:

When using colors, instead, we can have from a minimum of 3 bands, to a maximum of 6.

Here is the decoding chart to interpret the resistance value, the tolerance and, eventually, other information. You can find similar charts with a simple google search.


One last classification of resistors is based on the material used to make them. We can have:

  • carbon film resistors, made depositing a thin layer of carbon, usually graphite, on a ceramic or paper substrate
  • metal film resistors, made of a thin layer of metal deposited on a cylindrical support


The final, but not the least important, specification about resistors is their power dissipation capability or power rating. The power rating depends on the type of material they are made and the type of material of their support, as well as their size and the presence of a aluminum heat sink. the numbers can vary from 1/8W, going to 1/4W, 1/2W, 1W, and so forth, up to the hundreds of Watt.


When calculating the value of a resistor, never forget to calculate also the power it will need to dissipate, and always choose a resistor that can dissipate at least that amount of power.

For example, let’s get back to our example of resistor limiting the current in a LED. To calculate the power dissipation, we can use either one of these formulas:


n our example, we know the value of the resistor and the current that flows through it, so we can write:


Therefore we can use a resistor capable of dissipating 1/8W, equal to 0.25W, since its rating is greater than the actual dissipated power.


Don’t forget: always use a resistor with a rating higher than the calculated power, or the component may burn or even explode.

Conclusion


Well, now you know the theory behind resistance, how to use Ohm’s Law, how to calculate series and parallel equivalents, and how to physically identify the component you need.


In the next episode, we will dive deeper into the Kirchhoff’s Laws, which build on top of everything we covered today.

Happy experiments!!!

By the way: here is the link to the corresponding YouTube video, which you may want to watch for completeness: