Inductors in Parallel – Formula, Equivalent Inductance

Inductors in Parallel

Inductors in Parallel are a combination of inductors where terminals are connected to the same two nodes. An inductor is a passive electrical component that stores energy in its magnetic field. When the terminals of individual inductors are connected in parallel to each terminal of other inductors, they are said to be in parallel as shown below:

In the connection of Inductors in Parallel, the voltage across each inductor will be the same, and the current divided across the inductors. The least opposing inductor will have the maximum current through it. The reciprocal of equivalent inductance is the sum of the reciprocal of individual inductance present in the circuit.

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Equivalent Inductance of Inductors in Parallel

Consider the circuit of N inductors (neglecting the effect of mutual inductance) in parallel as shown below:

where L_eq is the equivalent inductance of inductors in parallel and i_eq(t₀) is the equivalent initial current through the equivalent inductor at time t₀

So, the equivalent inductance and equivalent initial current are given by,

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Inductors in Parallel Formula

The net equivalent inductance of N inductors in parallel is given by

Mutually Coupled Inductors in Parallel

The magnetic flux produced by the inductor links with other parallel-connected inductors. Due to the magnetic coupling between inductors in parallel, the equivalent inductance increases, or decreases based on whether the coils are of opposing or aiding in nature. Based on the direction of magnetic flux, inductors in parallel can be of two types:-

• Parallel aiding inductors: When the direction of magnetic flux produced by the inductors in parallel is in the same direction.
• Parallel opposing inductors: When the direction of magnetic flux produced by the inductors is in the opposite direction.

Parallel Aiding Inductors

Consider the following connection of Inductors in Parallel, where two inductors L₁ and L₂ are connected in parallel, for simplification, assuming two coils L₁ and L₂ connected in parallel with their magnetic flux aiding in nature as shown below. Let M be the mutual inductance between L₁ and L₂.

Applying KCL in the above circuit,

Now,

Parallel Opposing Inductors

Similarly, for parallel opposing inductors, consider two inductors L₁ and L₂ are connected in parallel, the equivalent inductance for two inductors L₁ and L₂ connected in parallel having mutual inductance M as shown below can be calculated as,

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