An inductor is a passive element which is used in electronics circuits for temporary storage of electrical energy in the form of magnetic flux or simply magnetic field. Inductance is the property of any coil which can sets up the magnetic flux when current passes through it.

Any device which has the property of inductance can be called an inductor. Usually inductor is built in the form of a coil with copper material around the core of a magnetic (iron) or nonmagnetic medium (like air).

## Inductors in Series

Assume that inductors connected in the circuit do not have any coupling between them. This implies that there are no flux lines from one inductor linking with another, and hence there will be no mutual flux between the coils.

The end to end connection of two or more inductors is called “series connection of inductors”. In this connection the inductors are connected in series so the effective turns of the inductor increases. The series connection of the inductors is shown in below diagram

The inductance of series connected inductors is calculated as the sum of the individual inductances of each coil since the current change through each coil is same.

This series connection is similar to that of the resistors connected in series, except the resistors are replaced by inductors. If the current I is flowing in the series connection and the coils are L1, L2, and so on, the common current in the series inductors is given by

I_{Total} = I_{L1} = I_{L2} = I_{L3}. . . = I_{n}

If the individual voltage drops across each coil in this series connection are VL1, VL2, V¬L3, and so on, the total voltage drop between the two terminals VT is given by

V_{Total} = V_{L1} + V_{L2} + V_{L3}…. + V_{n}

As we know that the voltage drop can be represented in terms of self inductance L, this implies

V = L di/ dt.

This can also be written as

LT di/dt = L1 di/dt + L2 di/dt + L3 di/dt + . . . + Ln di/dt

Therefore the total inductance is

L

_{Total}= L_{1}+ L_{2}+ L_{3}+ ….. + L_{n}

This means the total inductance of the series connection is the sum of individual inductances of all inductors. The above equation is true when there is no mutual inductance affect between the coils in this series configuration.

### Inductors Connected in Series Example

Ex 1: If a circuit has 3 inductors of 60 Henry, 30 Henry and 20 Henry connected in series, what will be the total inductance of the series?

We know that the formula for total inductance of series, L_{Total} = L_{1} + L_{2} + L_{3} + ….. + L_{n}

Given that L_{1} = 60 Henry

L_{1} = 30 Henry

L_{1} = 20 Henry

The total inductance, L_{Total} = 60 + 30 + 20 = 110 Henry.

### Summary

- An inductor is a passive element which is used in electronics circuits for storing energy as magnetic flux. Inductance is measured in Henry.
- The dissipation amount of actual power with the current flow in the circuit is called “Inductive reactance”. It is measured in ohms. X
_{L}= 2 f L - Self inductance is the property of an electric circuit or a loop in which its own magnetic field opposes any change in current

## Inductors in Parallel

Inductors are said to be connected in parallel when two terminals of an inductor respectively connected to each terminal of other inductors or inductor. Similar to the parallel connection of resistors, the total inductance in parallel connection of inductors is somewhat lesser than smallest inductance of an inductor in that connection.

If the inductors are connected in parallel, current chooses least opposition path of inductor when current in that circuit is decreased or increased while each inductor individually opposes that change (increase or decrease of current).

In the parallel connection, the voltage across each inductor is equal and also if the total current is changed, the voltage drop across each individual inductor will be less as compared with series connection. For a given rate of change of current, less will be the inductance in less voltage.

### Equation of Inductors connected in Parallel

We know that, in a parallel network the voltage remains constant and the current divides at each parallel inductor. If I_{L1}, I_{L2}, I_{L3} and so on I_{Ln} are the individual currents flowing in the parallel connected inductors L_{1}, L_{2} and so on L_{n}, respectively, then the total current in the parallel inductors is given by

I_{Total} = I_{L1} + I_{L2} + I_{L3} . . . . + I_{n}

If the individual voltage drops in the parallel connection are V_{L1}, V_{L2}, V_{L3} and so on V_{Ln}, then the total voltage drop between the two terminals V_{T} is

V_{Total} = V_{L1} = V_{L2} = V_{L3} . . . . = V_{n}

The voltage drop in terms of self inductance can be expressed as V = L di/ dt. This implies total voltage drop,

V_{T} = L_{T} di/dt

⇒ L_{T } d/dt (I_{L1} + I_{L2} + I_{L3} . . . . + In)

⇒ L_{T} ( (d_{i1})/dt + (d_{i2})/dt + (d_{i3})/dt . . . .)

Substituting V / L in place of di/dt, the above equation becomes

V_{T} = L_{T} (V/L_{1}+ V/L_{2} + V/L3 . . . .)

As the voltage drop is constant across the circuit, then v = V_{T}. So we can write

1/L_{T} = 1/L_{1} + 1/L_{2} + 1/L_{3} . . . . .

This means that the reciprocal of total inductance of the parallel connection is the sum of reciprocals of individual inductances of all inductors. The above equation is true when there is no mutual inductance is affect between the parallel connected coils.

If there is no mutual inductance between them, then the total inductance is given as

L

_{T}= (L_{1}× L_{2})/(L_{1}+ L_{2})

### Summary

- Connecting the two terminals of inductor respectively to other inductor or inductors terminals, then that connection is referred as “parallel connection of inductors”.
- When the fluxes produced by individual inductors are in the same direction, the mutual inductance will be increased; then these coils are called “Aiding” coils. Total inductance for aiding coils is L
_{T}= (L_{1}L_{2}– M^{2})/(L_{1}+ L_{2})-2M).When the fluxes produced by individual inductors are in the opposite direction of magnetic flux, the mutual inductance will be decreased; then these coils are called “opposing” coils. Total inductance for aiding coils is L_{T}= (L_{1}L_{2}– M^{2})/(L_{1}+ L_{2})+2M)