2Counter EMF (also known as Back EMF) When the current through an inductor changes, the magnetic field also changes. This changing magnetic field causes there to be an induced voltage across the terminals of the inductor. This induced voltage’s polarity is in a direction opposite to that of the original voltage applied.This is basically Lenz’s law in a nutshell.
3Current through inductors in a DC circuit when switch closes
4What do you think voltage across an inductor looks like in a DC circuit when the switch is closed?
5Voltage through inductors in a DC circuit when switch closes Inductance has it greatest effect only when there is a change in current.
7Inductance SummaryInductors react against changes in current by consuming or providing voltage in a polarity necessary to oppose the changeWhen an inductor is faced with an increasing current, it acts as a load, by consuming voltage. (series opposing)When an inductor is faced with a decreasing current, it acts as a source, by sourcing voltage. (series aiding)The ability of an inductor to store energy in the form of a magnetic field (and consequently opposing changes in current) is called inductance.The unit of inductance is the Henry – H (Denoted as the letter L on a schematic)
9Inductor Schematic Symbol Typically, the range of inductors are from micro-Henry’s to milli-Henry’s(H to mH)
10In the picture of the inductor below, since current takes the path of least resistance, why wouldn’t the current just bypass all the turning and jump straight across the tops of all the coils?Because there is a clear enamel coating on the wires that acts like an insulator
12Factors Affecting Coil Inductance N – Number of turnsThe design of the inductor is most important in determining the value of inductance.1. The amount of turns in creating the coil affect how much voltage can be linked between the turns. In a later equation, this figure is denoted by (N).
13Coil Inductance Factors (cont.) A – Area of coil2. The diameter of the coil affects inductance. A larger diameter core results in more magnetic lines of force than compared to a smaller diameter coil. Denoted by (A) for area=πr2.r
14Coil Inductance Factors (cont.) l – length of coil3. As the length (l) of the inductor grows, the distance between turns increases, which causes the magnetic field to get weaker.Denoted by l, for length in meters,not I for current!l
15Coil Inductance Factors (cont.) µ - permeability of core4. And finally, inductance is affected by the core material in which the coil is wrapped around. Higher permeability enables more flux to form. More flux means more inductance. This is denoted by (µ) pronounced “mju”, not known as micro in this case.Table 16.2 from bookMaterialPermeability, µ (H/m)Relative Permeability, µr (No Units)Air or Vacuum1.26 x 10-61Nickel6.28 x 10-550Cobalt7.56 x 10-560Cast Iron1.1 x 10-490Machine Steel5.65 x 10-4450Transformer iron core6.9 x 10-35500Silicon Iron8.8 x 10-37000Permalloy0.126100,000Supermalloy1.261,000,000
16Inductance equation 18.3.1 L= µN2A l L= Inductance in Henrys, H Table 16.2 from bookMaterialPermeability, µ (H/m)Relative Permeability, µr (No Units)Air or Vacuum1.26 x 10-61Nickel6.28 x 10-550Cobalt7.56 x 10-560Cast Iron1.1 x 10-490Machine Steel5.65 x 10-4450Transformer iron core6.9 x 10-35500Silicon Iron8.8 x 10-37000Permalloy0.126100,000Supermalloy1.261,000,000L= Inductance in Henrys, Hµ=permeability of core, µ0µrµ0= 1.26 x (The absolute permeability of air)µr= relative permeability of core material, refer to Table 16.2 N= number of coil turnsA= area of cross-section of coil wire, πr2.l= length of core material (m)
17Inductance problem worked out Given: l=10cm r=1.5cm N=200 turnsl= .1m r=.015m N=200 turnsIt’s an air core that we’re dealing with. So relative permeability is µr =1.L= (µ) (200)2 [π(.0152)].1L= µN2AlL= [(1.26 x 10-6)] (40000) ( ).1L= Hor356.3 µHL=.1
18Another Inductance problem! Given:l=15cmr=.02mN=500 turnsMachine Steel CoreFind Inductance Value
19Another Inductance problem! Given:l = 15cmr = .02mL = 3mHNickel CoreFind the number of turns
20Another Inductance problem! What is the inductance if you take a wire and wrap it around a pencil 15 times?
21Types of Inductors Types of Inductors Air Core Low value L High frequency applicationsIron-CoreLarge value LUsed in transformersPowdered iron-coreMid value LUsed to reduce losses such as eddy currents. Used for higher DC current applicationsFerrite CoreLow to High value LGreat Magnetic Conductor, Low Electrical Conductor. Suitable for high and low freq applicationsToroidal coreMid to High value LVery low flux leakage loss because of donut shape.Variable CoreVariable LUsed for tuning circuits like radiosPrinted Circuit board coreVery low LCoil printed Directly on circuit board. For Freq above 500Mhz (Very high
23Measuring the induced voltage across an inductor Equation 18.1:This equation says that the higher the change in current, and the faster that change occurs, the higher the voltage across the inductor will be.
24How much self-induced voltage occurs across a 4H inductor when the current going through it changes by 10Amps in 1 second?
25How much self-induced voltage occurs across a 4H inductor when the current going through it changes by 10Amps in 1ms?1ms)= 400V
26Calculating total inductance LT What is the total inductance of this circuit?62HCalculating the total inductance in a circuit is done the same way as calculating the total resistance
27Calculating total inductance LT What is the total inductance of this circuit?6HCalculating the total inductance in a circuit is done the same way as calculating the total resistance
28Calculating total inductance LT What is the total inductance of this circuit?LT = 15HCalculating the total inductance in a circuit is done the same way as calculating the total resistance
29THIS IS CALLED MUTUAL INDUCTANCE However! There is a subtle difference in calculating LT that you don’t have to consider when calculating RTWhat if the magnetic field from one inductor interferes with the magnetic field from the inductor next to it?In other words, if the magnetic field from one inductor cuts the across the coils of the inductor located physically next to it, then extra inductance will be introduced, (or some inductance will be cancelled out.)THIS IS CALLED MUTUAL INDUCTANCE
32Calculating total inductance if there is mutual inductance involved In the circuit above, if the inductor’s magnetic fields didn’t interfere with each other, aka have no mutual inductance, then the total inductance is just 13H.However, suppose the inductors magnetic fields were completely overlapping each other, then we would have to consider this.
33k is the coefficient of coupling and it is a number ranging from 0% to 100%If the coils of 2 inductors were wrapped around each other, then the magnetic fields of each have no choice but to couple themselves to the other inductor.In this case the coefficient of coupling, k, is 100%.If the inductors’ magnetic fields are not coupled, then k = 0.
35Calculating total inductance if there is mutual inductance involved Suppose the inductors were connected in a series aiding arrangement with a coefficient of coupling of 90%.
36Calculating total inductance if there is mutual inductance involved Suppose the inductors were connected in a series opposing arrangement with a coefficient of coupling of 90%.
372 coils have inductances of 8mH and 4. 7mH 2 coils have inductances of 8mH and 4.7mH. If the coefficient of coupling between them is .82, what is the mutual inductance?Now find the total inductance if they are series aiding and if theyare series opposingLT = 8mH mH + 2·5.03mH = 22.76mH (If in series aiding arrangement)LT = 8mH mH - 2·5.03mH = 2.64mH (If in series opposing arrangement)