# Inductors In Series Calculator

Created by Purnima Singh, PhD
Reviewed by Steven Wooding
Last updated: Aug 21, 2023

Use the inductors in series calculator to determine the equivalent inductance in a series circuit. If you often get confused between the circuits involving inductors in series and parallel, worry not! Continue reading to learn about adding inductors in series and the formula to calculate the total inductance of a series circuit. You will also learn the difference between the series and the parallel combination of inductors.

If you want to calculate the equivalent inductance in a parallel circuit, visit our inductors in parallel calculator.

## Inductors in series

We call a combination of inductors to be connected in series if the inductors are connected end to end with each other as shown in figure 1. If we connect an AC source across the two ends of this combination, the same current $I$ will flow through all the inductors, as there is no other path. However, the electromagnetic field (EMF) $e$ induced in each coil will depend on its inductance $L$.

In the following section, we will see how to add inductors in a series circuit.

## Formula for total inductance in a series circuit

When inductors are connected in series (see figure 1), the same current $I$ flows through each of them. The voltage, as well as the induced emf across each inductor, can be written using faraday's law formula as:

\scriptsize \begin{align*} e_1 &= L_1 \frac{dI}{dt}\\ e_2 &= L_2 \frac{dI}{dt}\\ .\\ .\\ e_n &= L_n \frac{dI}{dt}\\

\end{align*}

where, $e_1$, $e_2$, …, $e_n$ are the induced EMFs in the coils of inductance $L_1$, $L_2$, ..., $L_n$.

We can express the total potential across the combination ($e$) as:

$\scriptsize e = e_1 + e_2 + ... + e_n$

Using the formula for self-inductance, we can write:

\scriptsize \begin{align*} L\frac{dI}{dt} &= L_1 \frac{dI}{dt} + L_2 \frac{dI}{dt} + ... + L_n \frac{dI}{dt} \\ \\ \implies& L = L_1 + L_2 + ... + L_n \end{align*}

The above equation gives the formula for total inductance when inductors are connected in series. You might find this formula for total inductance in a series circuit familiar. It is because the resistors in a series circuit also adds in a similar way. Head on to our series resistor calculator to explore more!

## Adding inductors in series — an example

Let us see how to calculate the total inductance of a series circuit. Let $L_1 = 5\ \rm H$, $L_2 = 10\ \rm H$, and $L_3 = 15\ \rm H$.

1. We will use the formula for inductors in series, which is:

$L = L_1 + L_2 + L_3$.

2. Substituting the inductor values in the above equation, we get:

$L = 5 + 10 + 15$

$L = 30\ \rm H$

Hence, the total inductance of the given combination is 30 H.

## How to use the inductors in series calculator?

Now let us see how we can solve the same problem using our inductors in series calculator.

1. Choose the mode "Calculate equivalent inductance".

2. Type the inductance values, i.e., $L_1 = 5\ \rm H$, $L_2 = 10\ \rm H$, and $L_3 = 15\ \rm H$. You can add up to 10 inductors.

3. The calculator will display the equivalent inductance, i.e., $L = 30\ \rm H$.

4. You can also use the inductors in series calculator to find out the value of unknown inductance in a series circuit by changing the mode.

## Inductors in series and parallel — a comparison

The equivalent inductance offered by a circuit depends on how the individual inductors are connected in the circuit. We can identify the most simple combinations as series and parallel circuits. In the following section, we will try to understand the basic difference between the two.

• Arrangement in circuit: In series combination, the inductors are connected end to end with each other, whereas in parallel combination, one end of all the inductors is joined together at one point and the other end at another point.

• Current through each element: In a series circuit, the same current flows sequentially through each element. However, in parallel circuits the current through each element may be different as it is divided into different paths.

• EMF across each element: The EMF induced in each inductor in a series circuit is different, whereas in parallel circuits the same voltage is applied across each element and hence the same EMF is induced in each element.

• Equivalent inductance of the circuit: For a combination of n inductors, each with inductances $L_1$, $L_2$, ..., $L_n$, we can calculate the total inductance in series ($L_s$) and parallel ($L_p$) combinations as:

$L_s = L_1 + L_2 + ...+L_n$

…and:

$1/L_p = 1/L_1 + 1/L_2 + ...+ 1/L_n$.

## FAQ

### How do I find total inductance of a series circuit?

To find the total inductance of a series circuit, just add the inductance values of individual inductors.

### What is the inductance of three 10 mH inductors connected in series?

30 mH. The equivalent inductance of three 10 mH inductors connected in series is 10 mH + 10 mH + 10 mH = 30 mH.

### What happens when I connect two inductors in series?

When we connect two inductors of equal inductance in series, the equivalent inductance of the circuit is doubled. The current through each inductor remains the same, but the voltage across each inductor is halved.

### What is the basic principle of inductors?

The working principle of inductors is based on Faraday's law. It states that a time-varying current (or magnetic flux) induces an opposing EMF in the circuit, whose magnitude is directly proportional to the rate of change of current (or flux).

Purnima Singh, PhD Mode
Calculate equivalent inductance
Inductor 1 (L₁)
H
Inductor 2 (L₂)
H
You can add up to 10 inductors; fields will appear as you need them.
Results
Input at least one inductance to obtain a result.
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