This all-in-one online Inductors in Series Calculator finds the inductance of a circuit consisting of any number of inductors connected in series. It can also find the inductance of an inductor that needs to be connected in series with other inductors to get the necessary total inductance of this circuit.
You can enter the values of any known parameters in the input fields of this calculator and find the missing parameter. To add more inductors you can click the “+” symbol on the right hand side. You can also click the “–” symbol to delete extra lines.
Series Inductance Formula
Inductors are in series when they are connected head-to-tail so that the same amount of current flows through each of the inductors. Inductors in series can be represented as the following diagram, where \(L_{1}\), \(L_{2}\), …, \(L_{n}\) are the inductance values of the inductors connected in series.
An important property of a circuit consisting of inductors connected in series is that all the inductors have a common electric current \(I\) flowing through them. Further, according to Kirchhoff’s voltage law, the total voltage drop across the circuit \(V_{T}\) is equal to the sum of the individual voltage drops across each inductor \(V_{i}\):
$$V_{T} = V_{1} + V_{2} + … + V_{n}.$$
On the other hand, we know that the self-induced voltage across an inductor is given by the expression:
$$V_{i} = L_{i} \frac{dI}{dt},$$
where \(\frac{dI}{dt}\) is the rate of change of current in the circuit.
Thus, the total voltage drop across the circuit can be written as follows:
$$L_{T}\frac{dI}{dt} = L_{1}\frac{dI}{dt} + L_{2}\frac{dI}{dt} + … + L_{n}\frac{dI}{dt}.$$
And further reducing the common term with current in this expression, we get the formula for the total inductance of the circuit:
$$L_{T} = L_{1} + L_{2} + … + L_{n}.$$
In other words, the total inductance of all the inductors connected in series is equal to the sum of the inductances of these inductors.
In practice, it is sometimes necessary to find the inductance value of an inductor that should be connected in series with the existing inductor of known inductance to get the necessary total inductance.
The solution to any such problem can be easily found using our Inductors in Series Calculator.
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