INDUCTORS

INDUCTORS

An inductor, is a passive two-terminal electric component which resists changes in electric current passing through it. It consists of a conductor such as a wire, usually wound into a coil. When a current flows through it, energy is stored temporarily in a magnetic field in the coil. When the current flowing through an inductor changes, the time-varying magnetic field induces a voltage in the conductor, according to Faraday's law of electromagnetic induction,which opposes the change in current that created it.

An inductor consists of a coil of conducting wire.

If current is allowed to pass through an inductor, it is found that the voltage across the inductor is directly proportional to the time rate of change of the current. Using the passive sign convention,

where L is the constant of proportionality called the inductance.

Inductance is the property whereby an inductor exhibits opposition to the change of current flowing through it, measured in henrys(H).

The current-voltage relationship is obtained as,

The energy stored is, 

We should note the following important properties of inductor:

1. An inductor acts like a short circuit to DC.

2. The current through an inductor cannot change instantaneously.

3. The ideal inductor does not dissipate energy.

4. A practical, non-ideal inductor has a significant resistive component.

SERIES AND PARALLEL INDUCTORS:

Inductors in Series

Inductors can be connected together in either a series connection, a parallel connection or combinations of both series and parallel together, to produce more complex networks whose overall inductance is a combination of the individual inductors. However, there are certain rules for connecting inductors in series or parallel and these are based on the fact that no mutual inductance or magnetic coupling exists between the individual inductors.

                

 

The current, ( I ) that flows through the first inductor, L₁ has no other way to go but pass through the second inductor and the third and so on. Then, inductors in series have a Common Current flowing through them, for example:

                            I_L1 = I_L2 = I_L3 = I_AB …etc.

Inductors in series equation,

Then the total inductance of the series chain can be found by simply adding together the individual inductances of the inductors in series just like adding together resistors in series. However, the above equation only holds true when there is “NO” mutual inductance or magnetic coupling between two or more of the inductors.

Inductors in Parallel

Inductors are said to be connected together in “Parallel” when both of their terminals are respectively connected to each terminal of the other inductor or inductors. The voltage drop across all of the inductors in parallel will be the same. Then, Inductors in Parallel have a Common Voltage across them and in our example below the voltage across the inductors is given as:

                         V_L1 = V_L2 = V_L3 = V_AB …etc

In the following circuit the inductors L₁, L₂ and L₃ are all connected together in parallel between the two points A and B. 

 

Thus,

 Here, like the calculations for parallel resistors, the reciprocal ( 1/Ln ) value of the individual inductances are all added together instead of the inductances themselves. But again as with series connected inductances, the above equation only holds true when there is “NO” mutual inductance or magnetic coupling between two or more of the inductors. Where there is coupling between coils, the total inductance is also affected by the amount of coupling.