Electronics is a fascinating subject. We use countless electronic devices, appliances and gadgets in our everyday life. If you want to understand electronics, either to design a product yourself or to install or repair them, you have to start with the basics of electric system, circuits energy and power. One such basic concept is Series Circuit (the other being a Parallel Circuit). If you learn the basics of Series and Parallel Circuits, you can easily work on large complex circuit. In this guide, we will explore more about Series Circuits, Kirchhoff’s Voltage Law (KVL) and Voltage Divider concepts.

We already made a dedicated guide on Parallel Circuits and also a comparison of Series vs Parallel Circuits. Check the above links for more information.

Outline

Toggle## What is Series Circuit?

We already know from the previous tutorials that an electric circuit is combination of an energy source (voltage or current source), some components (resistors, capacitors, etc.) and metal conductors to connect them all. Electric Current flows from the energy source (such as a battery) to the load (such as a light bulb, which is essentially a resistor) through the conductors and the bulb glows.

What if we have two or more bulbs? How can we connect them to a single battery? There are a couple of basic ways you can connect two or more electronic components to an energy source. They are: Series and Parallel. You can also combine these two types into making a complex circuit but these two are the main.

In a Series Circuit, we connect all the components back-to-back in a ‘series’ fashion. Let us take the light bulb and battery example here as well. As the light bulb has two legs (or terminals or contacts), we connect the second leg of the first bulb to the first leg of the second bulb.

Then, we continue this i.e., the second leg of the second bulb to the first leg of the third bulb and so on. Finally, we connect the first leg of the first bulb and the second leg of the last bulb to the battery. This is the simplest explanation of a Series Circuit.

You can easily understand clearly with the help of the following circuit diagram. In this we have a battery and four light bulbs and all the light bulbs are “in series” with the battery.

## Characteristics of a Series Circuit

Let us understand the rules associated with a Series Circuit. For this, we shall use resistors as the circuit components as they the simplest of all. Assume there is a voltage source with three resistors in series.

There is only one path for the current to flow in the circuit.

As there is only one current path, same current flows through all the components of a series Circuit. For example, if I is the current in the circuit, then the current through all the resistors R_{1}, R_{2} and R_{3} is also I.

So, if I_{R1} is the current through R_{1}, I_{R2} is the current through R_{2} and I_{R3} is the current through R_{3}, then

**I = I _{R1} = I_{R2} = I_{R3}**

Next, the sum of voltage drops across all the components in a series circuit is equal to the source voltage. If V_{R1}, V_{R2} and V_{R3} are the voltage drops across R_{1}, R_{2} and R_{3} respectively and V is the Supply Voltage (or Source Voltage), then

**V = V _{R1} + V_{R2} + V_{R3}**

From Ohm’s Law, we know that the voltage drop across a component is equal to the product of current flowing through the component and its resistance.

**V = I × R**

We can apply this law to the above circuit.

**V = V _{R1} + V_{R2} + V_{R3}**

But according to Ohm’s Law,

**V _{R1} = I_{R1} × R_{1}**

**, V**_{R2}= I_{R2}× R_{2 }

**and V**_{R3}= I_{R3}× R_{3}Substituting these in the above equation, we get

**V = I _{R1} × R_{1} + I_{R2} × R_{2} + I_{R3} × R_{3}**

But the current in a series circuit is same. So,

**I _{R1} = I_{R2} = I_{R3} = I**

**V = I × R _{1} + I × R_{2} + I × R_{3}**

**V = I × (R _{1} + R_{2} + R_{3})**

For the sake of convenience, let us assume V is the supply Voltage, I is the total current in the circuit and R is the total resistance of the circuit. Then,

**V = I × R = I × (R _{1} + R_{2} + R_{3})**

Therefore,

**R = R _{1} + R_{2} + R_{3}**

The total resistance of resistors in series is equal to the sum of individual resistances.

## Different Components in Series Combination

Let us now see the equivalent values of different components in series.

### Resistors in Series

We already saw the result of resistors in series connection. The equivalent resistance is equal to the sum of individual resistances.

**R _{EQ} = R_{1} + R_{2} + R_{3}**

### Capacitors in Series

It is slightly different for capacitors in series. If C_{EQ} is the equivalent capacitance of three capacitors C_{1}, C_{2} and C_{3} in series, then

**1/C _{EQ} = 1/C_{1} + 1/C_{2} + 1/C_{3}**

### Inductors in Series

Finally, we have inductors. This is again same as the resistors i.e.; the total inductance is equal to the sum of individual inductances.

**L _{EQ} = L_{1} + L_{2} + L_{3}**

## Voltage Divider

An important concept in electrical and electronic circuits is Voltage Divider. We know that the voltage drop across the circuit components that are connected in series is equal to the product of its respective resistance and the current flowing through it.

Assume we have two resistors R_{1} and R_{2} that are connected in series as shown in the following image.

Here, V is the supply voltage, V_{R1} and V_{R2} are the voltage drops across R_{1} and R_{2} respectively. From the combination of Ohm’s Law and characteristics of Series Circuit, we get

**V = I × R = V _{R1} + V_{R2} = I×R_{1} + I×R_{2}**

Now, if we calculate the voltage across the second resistor R_{2},

**V _{R2} = V × R_{2} / (R_{1} + R_{2})**

Here, from the above equation, we can understand that the voltage across the second resistor R_{2} is a part of the input supply voltage. As the circuit essentially divides the input voltage between the two resistors, this circuit is known as Voltage Divider or Potential Divider Circuit.

This is an important technique to provide a low voltage that the supply voltage. For example, if we want to connect 5V and 3.3V devices (such as Arduino and a Bluetooth Module), we use such voltage dividers to reduce the 5V from Arduino down to 3.3V.

## Kirchhoff’s Voltage Law

Consider the previous example of three resistors in series with a power supply. The sum of voltage drops across these three resistors is equal to the supply voltage.

**V _{S} = V_{R1} + V_{R2} + V_{R3}**

By re-arranging the above equation, we get,

**V _{S} – V_{R1} – V_{R2} – V_{R3} = 0**

This is known as Kirchhoff’s Voltage Law or simply KVL. According to KVL, the algebraic sum of all the voltages in a closed loop is equal to zero.

## Applications of Series Circuits

An important application of Series Circuits is the holiday lights that we use in our homes for decoration. It consists of several light bulbs that are connected in series to the mains power supply. Since each bulbs have some voltage drop, we have to carefully design the series light bulbs so that all the bulbs have sufficient voltage.

From the previous explanation, we know there is only one path for the current to flow in a series connection and same current flows through all the bulbs. So, the problem with these series light bulbs is if any one bulb fails, the entire set doesn’t light up.

Another useful application of series connection is series battery connection. We know in a series circuit; the total voltage is the sum of individual voltages. So, of we connect two batteries in series, then we get the output as the sum of the battery voltages.

For example, you have two 12V batteries. If you connect them in series, then you have a 24V source at your disposal.

## Conclusion

A Series Circuit is one of the fundamental electric circuits. It is simply a back-to-back connection of all the components so that there is only one path for the current to flow. We saw the basic series circuit using light bulbs and resistors and also the characteristics of series circuits. After that, we take a look at two important concepts associated with series connection: Voltage Divider and Kirchhoff’s Voltage Law (KVL). Finally, we saw couple of important applications of Series Circuits.