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For a circuit to be considered a series circuit, circuit elements within the circuit must have a direct path, each joined in sequence — and the current path never forking, branching or splitting off into a separate path.

Simple Series Circuit

If we are using conventional current flow (area of positive charge to area of negative charge) and observing an example of a series circuit as shown below, we see that current flows from the positive terminal of the battery through a component (resistor) in the circuit — continuing its path through a load (LED), back towards the negative terminal of the battery, never splitting anywhere in the circuit. We see that the current can only flow through one path, never branching off somewhere else in the circuit.

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We Need a Way To Calculate Electrical Properties of Series Circuits

Later, we’ll be discussing series circuits for resistors — and we’ll want to know some of the electrical properties for this scenario. When working with series circuits, we’ll need a way to calculate the electrical properties of the circuit — such as voltage, current and resistance. This is where Ohm’s Law comes in to save the day!

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Ohm’s Law

If you’ve dabbled enough in your studies of circuits, you’ve bound to have come across Ohm’s Law. Ohm’s Law is a law that states the relationship between electric current and voltage potential. In short, Ohm’s Law says that for a given resistance and an electric current flowing through that resistance, there is a voltage potential across that resistance.

The formula for Ohm’s Law shows that for a given resistance, the product of the resistance (R) and the current (I) through that resistance are proportional to (equal to) the voltage potential (V) across that resistance:

\begin{equation}\label{eq:NL}
V = IR
\end{equation}

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Resistors in Series

Resistors in series are when two or more resistors are in sequence in a circuit — lined end-to-end, creating a single path for current to flow. The image below shows a simple circuit of three resistors in series connected to a battery.

Since we have three resistors in our circuit, we have three resistor values — but Ohm’s Law is written with only one R. What do we do?!

We see that each resistor — R₁, R₂ and R₃ — are valued at 1.2kΩ, 680Ω, and 1kΩ, respectively. Where Ω is the capital Greek letter for “Ohm” and 1kΩ is “one kilo-Ohm” or 1000Ω. Somehow, we’d like to combine these three resistor values so that we are only working with one resistor value. Since the resistors are in series, we just add them together! Resistors in series add.

\begin{equation}
R_1 + R_2 + R_3 = 1200Ω + 680Ω + 1000Ω = 2880Ω
\end{equation}

Let’s call “R₁ + R₂ + R₃” a different name, since “R₁ + R₂ + R₃” is a mouthful. Let’s call it R_eq to represent it as the equivalent resistance.

\begin{equation}
R_{eq} = R_1 + R_2 + R_3 = 2880Ω
\end{equation}

Now, we can rewrite Ohm’s Law using our newly acquired equivalent resistance:

\begin{equation}
V = IR = IR_{eq}
\end{equation}

So, now let’s plug-in the value for the equivalent resistance into V = IR_eq.

\begin{equation}
V = IR_{eq} = 2880I
\end{equation}

I’m writing V = 2880I, with the I behind 2880, because it’s visually more appealing than I2880 — know that the product of the two values are the same written either way. I’ve also left the unit Ω off of the resistance value.

Notice that in our circuit diagram for our series resistor above, we’re also given the value of the voltage source or battery voltage of 1.5V. If we wanted to, we could find the value of the current of the circuit above by rearranging our formula to find the circuit current.

\begin{equation}
V = 2880I
\end{equation}

\begin{equation}
\frac{V}{2880} = I
\end{equation}

\begin{equation}
I = \frac{V}{2880} = \frac{1.5V}{2880Ω} = 0.000521A = 0.521mA = 521µA
\end{equation}

So, by using Ohm’s Law on our series resistor circuit diagram above, we found the equivalent resistance to be 2880Ω — and since we were given the source voltage of the circuit, we were also able to find the circuit current to be 0.521 mA (milli-Amps) or 521 μA (micro-Amps).

We can see from the simulation image of our series resistor circuit below, that the ammeter (measures current in amps in a circuit) shows that our circuit current reads as being 521 μA — which is exactly what we calculated above! Yay!

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The Value of Current is the Same Throughout in Series Circuits

This next statement would be a fine point to remember. With the ability of the current to continue through a series circuit in its entirety without ever branching off anywhere means that the value of current is the same throughout the circuit. If you were to measure current with an ammeter, anywhere in the circuit, the value of the current would read the same everywhere.

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Series Circuits Are Voltage Dividers

If there’s a second thing that I could recommend you to absolutely remember out of everything mentioned here on series circuits, it’d be that series circuits are voltage dividers.

A series circuit being a voltage divider means that as current flows along the path of the series circuit and through components within the circuit, a voltage drop occurs across each component.

If we look at our series resistor circuit again, this time using a voltmeter (measures voltage in volts in a circuit), we see that there’s a voltage drop of different values across each resistor.

The voltage is divided down throughout the circuit, and the sum of those voltage divisions is the total voltage potential of the circuit’s power source — in this case, the battery voltage. So, looking at the image above, we see that across resistor R₁, there’s a voltage drop of 625 mV (milli-Volts). Across resistor R₂, there’s a voltage drop of 354 mV — and across resistor R₃, a voltage drop of 521 mV.

If we add all the voltage drops — V_R1, V_R2, V_R3 — across each resistor R₁, R₂ and R₃ — we should get the total supplied voltage to the circuit V_total, which is the battery voltage of 1.5V.

\begin{equation}
V_{Total} = V_{R1} + V_{R2} + V_{R3} = 625mV + 354mV + 521mV
\end{equation}

\begin{equation}
V_{Total} = 0.625V + 0.354V + 0.521V = 1.5V
\end{equation}

So, V_Total = 1.5V, which is the value of the battery voltage in our series resistor circuit!

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Conclusion

From our series resistor circuit example we observed above, we saw that we could find out quite a bit about the circuit’s electrical properties if we knew some preliminary values of the circuit — such as the resistor values and the value of the battery voltage — and if we knew Ohm’s Law and how to use it.

Series circuits are the simplest, most intuitive circuits to deal with in electronics. We learned that their paths are singular, never branching — allowing current to flow from the positive terminal of a battery to the negative terminal of a battery right through each component — and that the current is the same value throughout the circuit. We also learned that a series circuit is a voltage divider — meaning that as current flows along the path of the series circuit, a drop in voltage occurs across each component in the circuit and the sum of all the voltage drops is equal to the total voltage supplied to the circuit.

Now that you have a better insight into series circuits and how they work, you should have a greater confidence in your ability to understand these simple circuits, as well as in how to calculate values of electrical properties of a series circuit using Ohm’s Law. Your next step from here is to learn about parallel circuits. Remember to stay motivated and keep at it!