Inductors. In a circuit diagram, an inductor is shown like this:

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1 Inductors An inductor (also called a choke) is simply a coil of wire. It turns out, however, that a coil of wire can do some very interesting things because of the magnetic properties of a coil. There are many variations to the Inductor / Coil, below shows some of the variations. Inductors usually are categorized according to the type of inner core they are wound around, for example, hollow core (free air), solid iron core or soft ferrite core. The different core types are distinguished by adding continuous or dotted parallel lines next to the wire coil as shown below. In a circuit diagram, an inductor is shown like this: 1

2 An inductor is a passive electronic component which is capable of storing electrical energy in the form of magnetic energy. Basically, it uses a conductor that is wound into a coil, and when electricity flows into the coil from the left to the right, this will generate a magnetic field in the clockwise direction. The more turns with which the conductor is wound around the core, the stronger the magnetic field that is generated. A strong magnetic field is also generated by increasing the cross-sectional area of the inductor or by changing the core of the inductor 2

3 Let's now assume that an AC current is flowing through the inductor. "AC" (alternating current) refers to a current whose level and direction change cyclically over time. When current is about to flow to the inductor, the magnetic field generated by that current cuts across the other windings, giving rise to an induced voltage and thus preventing any changes in the current level. If the current is about to rise suddenly, an electromotive force is generated in the opposite direction to the current--that is, in the direction in which the current is reduced--thus preventing any increase in the current. Conversely, if the current is about to drop, an electromotive force is generated in the direction in which the current is increased. These effects of the induced voltage are produced even when the direction in which the current is flowing is reversed. Before overcoming the induced voltage that is attempting to block the current, the direction of the current is reversed so that there is no flow of current. The current level remains unchanged when DC (direct current) flows to the inductor so no induced voltage is produced, and it is possible to consider that a shorted state results. In other words, the inductor is a component that allows DC, but not AC, to flow through it. Summary 1. The inductor stores electrical energy in the form of magnetic energy. 2. The inductor does not allow AC to flow through it, but does allow DC to flow through it. 3

4 To understand how an inductor can work in a circuit, this figure is helpful: What you see here is a cell, a light bulb, a coil of wire around a piece of iron (yellow) and a switch. The coil of wire is an inductor. If you were to take the inductor out of this circuit, what you would have is a normal flashlight. You close the switch and the bulb lights up. With the inductor in the circuit as shown, the behavior is completely different. The light bulb behaves like a resistor (the resistance creates heat to make the filament in the bulb glow). The wire in the coil has much lower resistance (it's just wire), so what you would expect when you turn on the switch is for the bulb to glow very dimly. Most of the current should follow the low-resistance path through the loop. What happens instead is that when you close the switch, the bulb burns brightly and then gets dimmer. When you open the switch, the bulb burns very brightly and then quickly goes out. The reason for this strange behavior is the inductor. When current first starts flowing in the coil, the coil wants to build up a magnetic field. While the field is building, the coil inhibits the flow of current. Once the field is built, current can flow normally through the wire. When the switch gets opened, the magnetic field around the coil keeps current flowing in the coil until the field collapses. This current keeps the bulb lit for a period of time even though the switch is open. In other words, an inductor can store energy in its magnetic field, and an inductor tends to resist any change in the amount of current flowing through it. Henry This ability of an inductor to resist changes in current and which also relates current, with its magnetic field, as a constant of proportionality is called Inductance which is given the symbol L with units of Henry, (H) after Joseph Henry. 4

5 Because the Henry is a relatively large unit of inductance in its own right, we use smaller values for our inductors (milli Henry, micro Henry and nano Henry). Inductors or coils are very common in electrical circuits and there are many factors which determine the inductance of a coil such as the shape of the coil, the number of turns of the insulated wire, the number of layers of wire, the spacing between the turns, the permeability of the core material, the size or cross-sectional area of the core etc, to name a few.. Inductors in Series No Mutual inductance When inductors are connected in series, the total inductance is the sum of the individual inductors' inductances. L T = L 1 + L L N Example #1 Three inductors of 10mH, 40mH and 50mH are connected together in a series combination with no mutual inductance between them. Calculate the total inductance of the series combination. Inductors in Series Mutual inductance When inductors are connected together in series so that the magnetic field of one links with the other; this is referred to as mutual inductance. The effect of mutual inductance either increases or decreases the total inductance depending upon the amount of magnetic coupling. The effect of this mutual inductance depends upon the distance apart of the coils and their orientation to each other. Mutually connected inductors in series can be classed as either "Aiding" or "Opposing" the total inductance. If the magnetic flux produced by the current flows through the coils in the same 5

6 direction then the coils are said to be Cumulatively Coupled (diagram A). If the current flows through the coils in opposite directions then the coils are said to be Differentially Coupled (diagram B). Diagram A For Cumulative Coupling, The Total Inductance is given by: L T = L 1 + L 2 + 2M Where M refers to Mutual Inductance Diagram B For Differential Coupling, The Total Inductance is given by: L T = L 1 + L 2-2M Where M refers to Mutual Inductance Example #2 Two inductors of 10mH respectively are connected together in a series combination so that their magnetic fields aid each other giving cumulative coupling. Their mutual inductance is given as 5mH. Calculate the total inductance of the series combination. Example #3 Two coils connected in series have a self-inductance of 20mH and 60mH respectively. The total inductance of the combination was found to be 100mH. Determine the amount of mutual inductance that exists between the two coils assuming that they are aiding each other. 6

7 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 L 1, L 2 and L 3 are all connected together in parallel between the two points A and B. Example No1 Three inductors of 60mH, 120mH and 75mH are connected together in a parallel combination with no mutual inductance between them. Calculate the total inductance of the parallel combination. 7

8 Mutually Coupled Inductors in Parallel When inductors are connected together in parallel so that the magnetic field of one links with the other, the effect of mutual inductance either increases or decreases the total inductance depending upon the amount of magnetic coupling that exists between the coils. Mutually connected inductors in parallel can be classed as either "aiding" or "opposing" the total inductance with parallel aiding connected coils increasing the total equivalent inductance and parallel opposing coils decreasing the total equivalent inductance compared to coils that have zero mutual inductance. Mutual coupled parallel coils can be shown as either connected in an aiding or opposing configuration by the use of polarity dots or polarity markers as shown below. Parallel Aiding Inductors The voltage across the two parallel aiding inductors above must be equal since they are in parallel so the two currents, i 1 and i 2 must vary so that the voltage across them stays the same. Then the total inductance, L T for two parallel aiding inductors is given as: Where: 2M represents the influence of coil L 1 on L 2 and likewise coil L 2 on L 1. If the two inductances are equal and the magnetic coupling is perfect such as in a toroidal circuit, then the equivalent inductance of the two inductors in parallel is L as L T = L 1 = L 2 = M. 8

9 However, if the mutual inductance between them is zero, the equivalent inductance would be L 2 the same as for two self-induced inductors in parallel. If one of the two coils was reversed with respect to the other, we would then have two parallel opposing inductors and the mutual inductance, M that exists between the two coils will have a cancelling effect on each coil instead of an aiding effect as shown below. Parallel Opposing Inductors Then the total inductance, L T for two parallel opposing inductors is given as ^^ This time, if the two inductances are equal in value and the magnetic coupling is perfect between them, the equivalent inductance and also the self-induced emf across the inductors will be zero as the two inductors cancel each other out. This is because as the two currents, i 1 and i 2 flow through each inductor in-turn, the total mutual flux generated between them is zero because the two flux's produced by each inductor are both equal in magnitude but in opposite directions. Then the two coils effectively become a short circuit to the flow of current in the circuit so the equivalent inductance, L T becomes equal to ( L ± M ) 2. Example No2 Two inductors whose self-inductances are of 75mH and 55mH respectively are connected together in parallel aiding. Their mutual inductance is given as 22.5mH. Calculate the total inductance of the parallel combination. 9

10 Example No3 Calculate the equivalent inductance of the following inductive circuit. Calculate the first inductor branch, L A Calculate the second inductor branch, L B Calculate the equivalent circuit inductance, L EQ Then the equivalent inductance is 15mH. 10

11 Energy Stored in an Inductor Energy stored in an inductor is given by the formula: Time Constant of an Inductor When a current is applied to an inductor it takes some time for the current to reach its maximum value, after which it will remain in a "steady state" until some other event causes the input to change. The time taken for the current to rise to its steady state value (5τ) in an LR circuit depends on the time constant τ. Similar to Capacitors; τ represents the time taken for the inductor to charge to 63.2% of its final value. The resistance (R) - This is the total circuit resistance The inductance of L This is simply the equivalent Inductance. In a circuit which contains inductance (L), as well as resistance (R), such as the one shown in Fig..4.1, when the switch is closed the current does not rise immediately to its steady state value but rises in EXPONENTIAL fashion. This is due to the fact that a BACK EMF is created by the change in current flow through the inductor. This back EMF has an amplitude which is proportional to the RATE OFCHANGE of current (the faster the rate of change, the greater the back EMF) and a polarity which opposes the change in current in the inductor that caused it initially. The back EMF is produced because the changing current in the inductor causes a changing magnetic field around it and the changing magnetic field causes, in turn, an EMF to be induced back into the inductor. This process is called SELF INDUCTION. 11

12 Voltage across an Inductor Looking at the graph above, which shows the voltage (V L ) across the inductor (L) we can see that at switch on, the voltage immediately rises to a maximum value. This is because a voltage is being applied to the circuit and little or no current is flowing because L is effectively (for a very short time) a very high resistance due to the back EMF effect. The full supply EMF is therefore developed across the inductor. As current begins to flow through L however, the voltage V L decreases until a point is reached where the whole of the battery voltage is being developed across the resistor R and the voltage or potential difference (pd) across L is zero. When the current is switched off, the rapidly collapsing magnetic field around the inductor produces a large spike of induced current through the inductor in the opposite direction to the current that was flowing before switch off. These rapid changes in current as the switch opens can cause very large voltage spikes, which can lead to arcing at the switch contacts, as the large voltage jumps the gap between the contacts. The spikes can also damage other components in a circuit, especially semiconductors. Care must be taken to prevent these spikes that can occur in any circuit containing inductors. In some circuits however, where high voltage pulses are required, this effect can also be used to advantage. V L = LI 12