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4.12<\/p>\n
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- \n
- Understand the term ‘self inductance’ and recall that a ‘back EMF’ is produced as current flow changes in an inductor.<\/strong><\/em><\/li>\n<\/ul>\n
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Induced currents only ocur when a magnetic field builds or collapses.<\/p>\n
Lenz’s law tells us that the induced current is such as to oppose the change producing it.<\/p>\n
So the induced current will oppose the primary current when the field is building. Conversely, when the field is collapsing the current will be in the opposite direction to try to prevent the collapse.<\/p>\n
In the first instance the induced current field will be in a sense to oppose the primary current building. In the second instance when the field is collapsing, it will be in the same direction to lessen the collapse..<\/p>\n
![\"self](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/self-ind-diag01.jpg\")
<\/p>\nThe induced current is produced by a ‘back EMF’ – an induced voltage proportional to minus the rate of primary current change.<\/p>\n
![\"self](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/self-ind-eq00.jpg\")
<\/p>\n![\"self](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/self-ind-eq01.jpg\")
<\/p>\nwhere\u00a0<\/span>L<\/strong><\/em>\u00a0<\/span>(the inductance) is the constant of proportionality.<\/p>\n
Rearranging to make\u00a0<\/span>L<\/strong><\/em>\u00a0<\/span>the subject of the equation. By making\u00a0<\/span>E<\/strong><\/em>\u00a0<\/span>and\u00a0<\/span>dI\/dt<\/strong><\/em>\u00a0<\/span>unity we define the unit of self induction, the\u00a0<\/span>henry<\/strong>:<\/p>\n
![\"definition](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/self-ind-eq000b.jpg\")
\u00a0<\/p>\nA coil has a self inductance of\u00a0<\/span>1 henry<\/u>\u00a0<\/span>(H) if the back EMF is\u00a0<\/span>1 volt<\/u>\u00a0<\/span>for a current change of\u00a0<\/span>1 ampere\/second<\/u>.<\/strong><\/p>\n
By equating the EMF from Neumann’s equation with self induction EMF a simplified expression linking the two can be formed.<\/p>\n
![\"self](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/self-ind-eq02.jpg\")
<\/p>\nIntegrating between the limits of\u00a0<\/span>\u03c6<\/strong>\u00a0<\/span><\/em>– 0 and\u00a0<\/span>I<\/strong><\/em>\u00a0<\/span>– 0 ,<\/p>\n
![\"self](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/self-ind-eq03.jpg\")
<\/p>\n![\"self](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/self-ind-eq04.jpg\")
<\/p>\nMutual Induction<\/u><\/strong><\/p>\n
Mutual induction concerns a pair of coils. A building current in one coil (the primary) produces a building magnetic field around it. This in turn induces a building current to flow in the other coil. The induced current flow is in such a direction as to produce a magnetic field direction to oppose the primary magnetic field. The magnetic fields are directed towards each other. So their total effect is reduced.<\/p>\n
<\/a>
![\"mutual](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/mut-ind-diag01.jpg\")
<\/p>\nWhen the primary current direction is reversed its magnetic field direction is also reversed. This has the effect of making current in the secondary reverse direction together with its magnetic field direction. In this case the magnetic fields are in opposing directions.<\/p>\n
As with self inductance, the back EMF is proportional to minus the rate of current change. However, in this case the back EMF is in the secondary coil, not and in the primary(as with self induction).<\/p>\n
<\/p>\n![\"mutual](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/mut-ind-eq01.jpg\")
<\/p>\nWhere\u00a0<\/span>M<\/strong><\/em>\u00a0<\/span>(mutual inductance) is the constant of proportionality.<\/p>\n
There is another important link between self and mutual inductance. It can be shown, assuming 100% flux linkage that,<\/p>\n
![\"mutual](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/mut-ind-eq02.jpg\")
<\/p>\nwhere\u00a0<\/span>Lp<\/sub><\/strong><\/em>\u00a0<\/span>and\u00a0<\/span>Ls<\/sub><\/strong><\/em>\u00a0<\/span>are respectively the self inductances of primary and secondary coils.<\/p>\n
So the back EMF\u00a0<\/span>Es<\/sub><\/strong><\/em>\u00a0<\/span>in the secondary coil relates to the rate of current change\u00a0<\/span>dIp<\/sub>\/dt<\/strong><\/em>\u00a0<\/span>in the primary.<\/p>\n
![\"mutual](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/mut-ind-eq03.jpg\")
<\/p>\nThe secondary back EMF also relates to the rate of change of flux linkage in the secondary.<\/p>\n
![\"mutual](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/mut-ind-eq04.jpg\")
<\/p>\nElimenating\u00a0<\/span>Es<\/sub><\/strong><\/em>\u00a0<\/span>from these two expressions,<\/p>\n
![\"mutual](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/mut-ind-eq04b.jpg\")
<\/p>\nIntegrating between the limits of\u00a0<\/span>\u03c6s<\/sub><\/strong>\u00a0<\/span><\/em>– 0 and\u00a0<\/span>Ip<\/sub><\/strong><\/em>\u00a0<\/span>– 0 ,<\/p>\n
![\"mutual](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/mut-ind-eq04c.jpg\")
\u00a0<\/p>\n![\"mutual](\"https:\/\/www.a-levelphysicstutor.com\/images\/fields\/mut-ind-eq05.jpg\")
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4.13<\/p>\n
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- \n
- Recall that the inductance of a coil increases with increasing number of turns, increasing coil diameter and decreasing spacing between turns.<\/strong><\/em><\/li>\n
- Understand the use of high permeability cores and slug tuning.<\/strong><\/em><\/li>\n<\/ul>\n
[\/et_pb_text][et_pb_toggle title=”Factors affecting inductance” _builder_version=”4.9.10″ _module_preset=”default” title_font=”|700|||||||” title_font_size=”14px” custom_padding=”10px|||||” hover_enabled=”0″ sticky_enabled=”0″]<\/p>\n
To increase the property of\u00a0<\/span>inductance<\/a>, the conductor can be formed into a loop or coil. A coil is also called an inductor. Figure 2-3 shows a conductor formed into a coil. Current through one loop produces a\u00a0<\/span>magnetic field<\/a>\u00a0that encircles the loop in the direction as shown in figure 2-3(A). As current increases, the\u00a0<\/span>magnetic field<\/a>\u00a0expands and cuts all the loops as shown in figure 2-3(B). The current in each loop affects all other loops. The field cutting the other loop has the effect of increasing the opposition to a current change.<\/span><\/p>\n
Figure 2-3. – Inductance.<\/p>\n
![\"32NE0136.GIF](\"http:\/\/www.tpub.com\/neets\/book2\/32NE0136.GIF\")
<\/p>\nInductors are classified according to core type. The core is the center of the inductor just as the core of an apple is the center of an apple. The inductor is made by forming a coil of wire around a core. The core material is normally one of two basic types: soft-iron or air. An iron-core inductor and its schematic symbol (which is represented with lines across the top of it to indicate the presence of an iron core) are shown, in figure 2-4(A). The air-core inductor may be nothing more than a coil of wire, but it is usually a coil formed around a hollow form of some nonmagnetic material such as cardboard. This material serves no purpose other than to hold the shape of the coil. An air-core inductor and its schematic symbol are shown in figure 2-4(B).<\/p>\n
Figure 2-4. – Inductor types and schematic symbols.<\/p>\n
![\"32NE0137.GIF](\"http:\/\/www.tpub.com\/neets\/book2\/32NE0137.GIF\")
<\/p>\nFactors Affecting Coil Inductance There are several\u00a0<\/span>physical factors<\/a>\u00a0<\/span>which affect the inductance of a coil. They include the number of turns in the coil, the diameter of the coil, the coil length, the type of material used in the core, and the number of layers of winding in the coils.<\/p>\n
Inductance depends entirely upon the physical construction of the circuit, and can only be measured with special laboratory instruments. Of the factors mentioned, consider first how the number of turns affects the inductance of a coil. Figure 2-5 shows two coils. Coil (A) has two turns and coil (B) has four turns. In coil (A), the flux field set up by one loop cuts one other loop. In coil (B), the flux field set up by one loop cuts three other loops. Doubling the number of turns in the coil will produce a field twice as strong, if the same current is used. A field twice as strong, cutting twice the number of turns, will induce four times the\u00a0<\/span>voltage<\/a>. Therefore, it can be said that the\u00a0<\/span>inductance varies as the square of the number of turns<\/u>.<\/p>\n
<\/p>\n
Figure 2-5. – Inductance factor (turns).<\/p>\n
![\"32NE0138.GIF](\"http:\/\/www.tpub.com\/neets\/book2\/32NE0138.GIF\")
<\/p>\nThe second factor is the coil diameter. In figure 2-6you can see that the coil in view B has twice the diameter of coil view A. Physically, it requires more wire to construct a coil of large diameter than one of small diameter with an equal number of turns. Therefore, more lines of force exist to induce a counter emf in the coil with the larger diameter. Actually, the inductance of a coil\u00a0<\/span>increases directly as the cross-sectional area of the core increases<\/u>. Recall the formula for the\u00a0<\/span>area of a circle<\/a>: A =\u00a0<\/span>p<\/span>r2<\/sup>. Doubling the radius of a coil increases the inductance by a factor of four.<\/p>\n
Figure 2-6. – Inductance factor (diameter).<\/p>\n
![\"32NE0139.GIF](\"http:\/\/www.tpub.com\/neets\/book2\/32NE0139.GIF\")
<\/p>\nThe third factor that affects the inductance of a coil is the length of the coil. Figure 2-7 shows two examples of coil spacings. Coil (A) has three turns, rather widely spaced, making a relatively long coil. A coil of this type has few flux\u00a0<\/span>linkages<\/a>, due to the greater distance between each turn. Therefore, coil (A) has a relatively low inductance. Coil (B) has closely spaced turns, making a relatively short coil. This close spacing increases the flux linkage, increasing the inductance of the coil.\u00a0<\/span>Doubling the length of a coil while keeping the same number of turns halves the value of inductance<\/u>.<\/p>\n
Figure 2 – 7. – Inductance factor (coil length). CLOSELY WOUND<\/p>\n
![\"32NE0140.GIF](\"http:\/\/www.tpub.com\/neets\/book2\/32NE0140.GIF\")
<\/p>\nThe fourth physical factor is the type of core material used with the coil. Figure 2-8 shows two coils: Coil (A) with an air core, and coil (B) with a soft-iron core. The magnetic core of coil (B) is a better path for magnetic lines of force than is the nonmagnetic core of coil (A). The soft-iron magnetic core’s high permeability has less reluctance to the magnetic flux, resulting in more magnetic lines of force. This increase in the magnetic lines of force increases the number of lines of force cutting each loop of the coil, thus increasing the\u00a0<\/span>inductance<\/a>\u00a0<\/span>of the coil. It should now be apparent that the\u00a0<\/span>inductance of a coil increases directly as the permeability of the core material increases<\/u>.<\/p>\n
Figure 2-8. – Inductance factor (core material). SOFT-IRON CORE<\/p>\n
![\"32NE0141.GIF](\"http:\/\/www.tpub.com\/neets\/book2\/32NE0141.GIF\")
<\/p>\nAnother way of increasing the inductance is to wind the coil in layers. Figure 2-9 shows three cores with different amounts of layering. The coil in figure 2-9(A) is a poor inductor compared to the others in the figure because its turns are widely spaced and there is no layering. The\u00a0<\/span>flux<\/a>\u00a0<\/span>movement, indicated by the dashed arrows, does not link effectively because there is only one layer of turns. A more inductive coil is shown in figure 2-9(B). The turns are closely spaced and the wire has been wound in two layers. The two layers link each other with a greater number of flux loops during all flux movements. Note that nearly all the turns, such as X, are next to four other turns (shaded). This causes the\u00a0<\/span>flux<\/a>\u00a0<\/span>linkage to be increased.<\/p>\n
Figure 2-9. – Coils of various inductances.<\/p>\n
![\"32NE0142.GIF](\"http:\/\/www.tpub.com\/neets\/book2\/32NE0142.GIF\")
<\/p>\nA coil can be made still more inductive by winding it in three layers, as shown in figure 2-9(C). The increased number of layers (cross-sectional area) improves flux linkage even more. Note that some turns, such as Y, lie directly next to six other turns (shaded). In actual practice, layering can continue on through many more layers. The important fact to remember, however, is that\u00a0<\/span>the inductance of the coil increases with each layer added<\/u>.<\/p>\n
As you have seen, several factors can affect the inductance of a coil, and all of these factors are variable. Many differently constructed coils can have the same inductance. The important information to remember, however, is that\u00a0<\/span>inductance is dependent upon the degree of linkage between the wire conductor(s) and the\u00a0<\/span>electromagnetic field<\/a><\/u>. In a straight length of conductor, there is very little flux linkage between one part of the conductor and another. Therefore, its inductance is extremely small. It was shown that conductors become much more inductive when they are wound into coils. This is true because there is maximum flux linkage between the conductor turns, which lie side by side in the coil.<\/p>\n
<\/a><\/p>\n
- Understand the use of high permeability cores and slug tuning.<\/strong><\/em><\/li>\n<\/ul>\n
- Recall that the inductance of a coil increases with increasing number of turns, increasing coil diameter and decreasing spacing between turns.<\/strong><\/em><\/li>\n