Parallel Inductor

Let us see some of the properties of inductors in parallel configuration.

Connection

Total Inductance in Parallel

A parallel inductor connection has been shown above. Notice how one end of the inductors is connected to one common point and the other end is connected to another common point resulting in the same potential development across each. Due to this form of connection, the voltage developed is the same across all inductors.

Total inductance in Parallel

Let us see the derivation of the mathematical equation seen above for inductors in parallel.

From the above circuit diagram, we can see that the voltage developed across each inductor is the same. We can calculate the total current as the sum of current across each inductor

From KCL i = i₁ + i₂ eq 1

The Voltage Across Each Inductor

In parallel, circuit the voltage across each inductor will be the same and we, denote it by V in the derivation

Current and Flux Linkage

The current across each inductor can be given by the following equation

i_L = 1 / L ∫V.dt

If we assume the initial conditions to be zero, we can write the equation 1 as

i = 1 / L₁ ∫V.dt + 1 / L₂ ∫V.dt eq 2

where total current can be represented in terms of L_eq as

i = 1 / L_eq ∫V.dt eq 3

On comparing eq 2 and eq 3

1 / L_eq ∫V .dt = 1 / L₁ ∫V.dt + 1 / L₂ ∫V.dt ∴ 1 / L_eq = 1 / L₁ + 1 / L₂

Clearly, for N inductors we can say that

1 / L_eq = 1 / L₁ +1 / L₂ + 1 / L₃ ……………………………… 1 / L_n

Inductors are an important device used in electronics engineering for circuit designing and analysis. There are different configurations in which we can place an inductor two of the most important of which are series and parallel. In this article, we will study series and parallel inductor.

We will see the inductance, current, and flux linkage in each type of circuit. We will also see the total inductance in each case and discuss the concept of mutual inductance. Later, we will study the applications of each type of circuit. We will also see some examples to enhance the understanding of the concepts. The article concludes with some frequently asked questions that readers can refer to.