# ATAT 105 Basic Electricity > # [[T105 Week 8| ◀️ ]]  [[T105 Home| Home ]]  [[T105 Week 10| ▶️ ]]               [[QR T105 Week 9| 🌐 ]] ># [[T105 Week 9|Week 9]] >- [[T105 Week 9#ElectroMagnetism|ElectroMagnetism]] >- [[T105 Week 9#Inductance|Inductance]] ># [[T105 Week 9#Lab|Lab]] >- [[MP105 1|🔵MP 105-1]] >[!jbplus|c-blue]- Lesson Intro >### What >In this lesson you will learn about inductors in preparation for learning about alternating current. > >### Why > >The dynamic aspect of inductors must be understood in order to analyze Alternating Current circuits. > > >## Approach and Objectives > >By understanding the following topics, you will have achieved the learning outcome for this lesson. Consult your course outline for the learning outcomes and other details of this course. > >### Course Learning Objectives > >CLO 13. Compute the peak, instantaneous and effective (RMS) values of an AC sine wave. >CLO 14. Show using an oscilloscope the measurement of frequency, period and voltage of an AC waveform. >CLO 17. Calculate total inductance in series and parallel inductive circuits. > > >### Testing > >You will be tested on this material on the midterm test and the final test. Details [[T105 Intro#Testing and Grades|here]]. >[!jbplus|c-blue]- Prof >### Objectives > >In this lesson we will learn about inductors in order to prepare students for AC circuit analysis > > ### Theory >For the theory course, magnetism and inductors >### Lab >For the lab, [[MP105 1|MP 105-1.]] ## ElectroMagnetism ### Magnetism One of the most effective devices used to produce electricity is the magnet. By definition, a magnet is a body that has the ability to attract ferrous substances and produce an external magnetic field. ![[Pasted image 20210808135454.png|350]] It is these magnetic fields that are of interest in the study of electricity. The ends of the magnet are called the poles, and are referred to as the north- and south-seeking poles. [[Birds and Magnetism|‼]] ![[Pasted image 20210808135528.png|350]] #### Inverse Square Law of Repulsion and Attraction Magnetism follows the same rules as charges of static electricity. Like poles repel each other, and the force of repulsion follows the inverse square law. This means that if the distance between the poles is doubled, the force of repulsion is reduced to one-fourth as we saw [[T105 Week 1#Static Electricity|here]]. ![[Pasted image 20210808135709.png|350]] On the other hand, the force of attraction is squared as the distance decreases by 1/2. In other words, when you decrease the separation by half, the force of attraction increases four times. ![[Pasted image 20210808135725.png|350]] #### Magnetic Flux A magnet produces an external magnetic field. The magnetic field consists of invisible lines called lines of magnetic flux. Lines of flux are always complete loops that leave the north-seeking pole of the magnet at right angles to its surface and re-enter the south pole in the same fashion. ![[Pasted image 20210808135751.png|350]] The inside of a piece of unmagnetized iron contains an almost infinite number of magnetic fields oriented in a random fashion. However, if a piece of iron is placed in a strong magnetic field, all of the fields, or domains, align themselves with the induced magnetic field. Once this occurs, the iron becomes a magnet having a north and south pole and lines of magnetic flux. ![[Pasted image 20210808135827.png|350]] The domain theory of magnetism is supported by the fact that each magnet has both a north and south pole, regardless of the size of the magnet. For example, if you break a bar magnet in two, each half demonstrates the characteristics of the original magnet. If you break each of these halves in two, all of the pieces still retain magnetic properties. ![[Pasted image 20210808135946.png|350]] #### Retentivity Retentivity is the ability of a substance to retain or resist magnetization, frequently measured as the strength of the magnetic field that remains in a sample after removal of an inducing field. Soft iron has a very low retentivity. As soon as a magnetizing force is removed, the domains lose their alignment and the iron loses its magnetism. On the other hand, materials such as hard steel and some iron alloys have very high retentivities, retaining their magnetic properties long after they are magnetized. Materials with high retentivity are used as permanent magnets in aircraft magnetos, instruments, and radio speakers. #### Residual Magnetism Residual Magnetism is the magnetism left behind in a ferromagnetic material like iron after an external magnetic field is removed. #### Permeability As lines of flux travel from the north pole to the south, they always follow the path of least resistance. The measure of ease with which lines of flux travel through a material is referred to as a material's permeability. Air is used as a reference and is given the permeability value of one. ![[Pasted image 20210808140017.png|350]] Since flux travels through iron much easier than through air, its permeability is around 7,000. Other materials such as copper and aluminum have permeabilities considerably lower than iron. Some of the extremely efficient permanent magnet alloys have permeability values as high as 1,000,000. One way to shield an object from magnetic fields is to enclose it in a shield made of a highly permeable material. The lines of flux flow through the shield and bypass its centre. ![[Pasted image 20210808140234.png|350]] ### Magnetism and Electricity If a conductor is moved through the lines of magnetic flux that pass between the poles of a magnet, a flow of electrons is induced in the conductor. This property is known as Faraday's Law. This is called electromagnetic [[Inductance|inductance]] and is the most common form of electric power generation in use today. Most aircraft use generators or alternators to produce electricity by this method. ![[Pasted image 20210808140312.png|350]] In fact, atomic, hydro-electric, and fossil fuel power plants produce power by the same procedure. The amount of electricity induced depends on the rate at which the lines of flux are cut. This rate can be increased by - increasing the number of flux lines - making the magnet stronger, or - moving the conductor through the lines faster. Although the effects of magnetism had been observed for centuries, it was not until 1819 that the relationship between electricity and magnetism was discovered. We have just seen that a conductor that crosses lines of flux will have current induced in itself. Interestingly and importantly, the opposite process is also true. When current flows through a conductor, it produces a magnetic field that surrounds the conductor. ![[Pasted image 20210808140624.png|350]] You can see the magnetic field produced by a conductor by sprinkling iron filings on a plate that surrounds a current-carrying conductor. When this is done, the filings arrange themselves in a series of concentric circles around the conductor. ![[Pasted image 20210808140826.png|350]] The reason for this is when electrons travel through a conductor, they produce lines of flux. The greater the amount of flow, the stronger the magnetic field. ![[Pasted image 20210808150510.png|350]] #### Left Hand Rule for Single Conductors One way to determine the direction the lines of flux travel is with the left-hand rule for single conductors. For example, if you grasp the conductor in your left hand with your thumb pointing in the direction of electron flow, your fingers encircle the conductor in the direction of the lines of flux travel. ![[Pasted image 20210808150635.png|350]] ### The Effect of Coils Because the magnetic field around a conductor does not have any poles and is relatively weak, it does not serve a practical purpose. However, if the conductor is wound into the form of a coil, the lines of flux become concentrated inside the coil and the coil attains the characteristics of a magnet. ![[Pasted image 20210808150723.png|350]] The lines of flux become more dense and all are in the same direction strengthening the field. ![[Pasted image 20210808150750.png|350]] Electrons flow into the coil from the right. As the conductor passes over the top of the coil, the electrons flow away from you, as indicated by the cross representing the tail of the arrow. Below the coil, the electrons flow toward you, as indicated by the dot representing the head of the arrow. When the electron flow is away from you, the lines encircle the conductor in a counterclockwise direction. When they come toward you, the field circles the conductor clockwise. The lines of flux surrounding each turn of wire reinforce the flux around every other turn of wire. This results in a magnetic field that leaves the north end of the coil and enters the south end. Because this magnetic field is created by the electromotive force running through the coil, this device is called an electromagnet. ![[Pasted image 20210808150831.png|350]] #### Left Hand Rule For Coils To determine which end of an electromagnet is north and which is south, you can use the left-hand rule for coils. ![[Pasted image 20210808150954.png|350]] This rule states that if you grasp a coil with your left hand so your fingers wrap around the coil in the direction of electron flow, your thumb points to the coil's north pole. #### Strength of Electromagnets The strength of an electromagnet is determined by the: - number of turns in the coil - amount of current flowing through it - type of material used for a core ![[Pasted image 20210808151354.png|350]] Adding an iron core will increase the permeability of the inside of the coil, increase the flux density at the center of the coil and at the same time magnetizing the the iron core. The coil is now an electromagnet with an iron core. If the magnetic field is strong enough, the iron bar will be drawn into the coil until it is approximately centered in the magnetic field. An application of the movement of an iron core within a coil due to the magnetic field is a solenoid. ![[Pasted image 20210808151448.png|350]] #### Magnetomotive Force Magnetomotive force is the magnetic effect that causes a magnetic field (flux) to be produced. It is abbreviated MMF. ![[Pasted image 20210808151528.png|350]] Magnetomotive force can be measured in ampere-turns (At) or in Gilberts (G). These units are not equal though. It's like one mile vs one kilometer, the conversion in this case being 1 Gilbert is equal to .7968 ampere-turns. One ampere-turn is the measurement of one ampere (1A) flowing in a single coil or loop of wire in a vacuum. Turns refers to coils or loops, so ampere-turns are the product of the current (amperes) multiplied by the number of coils (turns) in the coil. In effect, ampere-turns are a measure of the magnetizing or demagnetizing strength of the coil. The magnetic field of a simple coiled conductor can be compared to a simple electrical circuit. The ampere-turns of magnetomotive force (mmf) produce the magnetic flux (Φ). The mmf compares to the emf or voltage in a simple electrical circuit. The flux compares to the current in a simple electrical circuit. #### Reluctance The reluctance compares to the resistance in a simple electrical circuit. Reluctance (R) (rel) is the opposition in a circuit to the flow of magnetic flux and is inversely proportional to permeability. Ohm's Law for magnetic circuits corresponds to I = V / R and is expressed as Φ = mmf / R ## Inductance > [!aside]- Ref >[[Inductance|🗺️]] ### Lenz' Law Lenz' Law can be understood as the electrical version of Newton's 3rd law: - for every action there is an equal and opposite reaction When the current in a wire changes, the magnetic field expands or contracts. As it does, the lines of flux cross the conductor and induce a voltage of opposite polarity. ![[Pasted image 20210808175822.png|350]] This induced opposing voltage is called a counter-electromotive force or counter EMF. As the voltage begins to rise and the current increases, the expanding lines of flux cut across the conductor and induce a voltage that opposes, or slows down, the rising voltage. When the current flow in a conductor is steady, the lines of flux do not cut across the conductor and induce a voltage, so there is no counter EMF. When the current decreases, the lines of flux cut across the conductor as they collapse and induce a voltage that opposes the decrease. Inductance is the behavior of a coil of wire in resisting any change of current through the coil. ### Units of Inductance The symbol for inductance is L and is measured in Henrys. One Henry of inductance generates one volt of induced voltage when the current changes at the rate of one ampere per second. All conductors have the characteristic of inductance since they all generate a back voltage any time the current flow changes. But remember that if conductors are not in a coil, this effect is virtually negligible. Inductance is much more a factor when the conductor is formed into a coil. ### Factors Affecting Inductance Anything that concentrates the lines of flux or causes more flux lines to cut across the conductor increases the amount of inductance. For example, if a conductor is formed into a coil, the lines of flux surrounding any one of the turns cut not only across the conductor itself, but across each of the turns as well. ![[Pasted image 20210808180047.png|350]] Therefore, a much greater induced current is generated to oppose the source current. If a soft iron core is inserted into a coil, it further concentrates the lines of flux. We learned about that [[T105 Week 9#Permeability|earlier]]. ![[Pasted image 20210808180108.png|350]] This causes an even higher inductance (higher induced current) and allows even less source current to flow. When you study, and you come across this graphic, ensure that you understand each of the effects, and whether they increase or decrease the inductance. ![[Pasted image 20210808180126.png|350]] Inductance is determined by: - The number of turns in the coil - The spacing of the turns - The number of layers of winding - Wire size - The ratio of coil diameter to length - Core material Since all of these factors are variable there is no simple formula to determine a coil's inductance. ### Construction ![[Pasted image 20210808180203.png|350]] Inductors are another component found in circuits and may be connected in the same manner as resistors. Coils are wound on a spool or bobbin. The wire used has a very thin enamel insulation - the voltage from turn to turn is very low, so not much insulation is needed. If different windings need insulation between them (like in a transformer) an insulating film or Nomex is often used. Cores are typically added afterwards. ### Inductors in Series ![[Pasted image 20210808180321.png|350]] If the inductors are connected in series such that the changing magnetic fields do not affect each other the total inductance is the sum of the individual inductors. ### Inductors in Parallel ![[Pasted image 20210808180427.png|350]] If the inductors are connected in parallel such that the changing magnetic fields do not affect each other the total inductance is calculated the same way as for parallel resistors. This also means that the total inductance will be less than the smallest inductance. This is a function of the formula. ![[Pasted image 20210808180442.png|350]] If the inductors are mounted such that their fields interfere with each other, the interplay becomes very complex, and again, there is no simple formula for this. Designers tend not to mount inductors where this is possible. ### Current/Voltage Phase Shift ![[Pasted image 20231113051610.png|350]] When a voltage source is applied to an inductor, the current does not rise instantly. For example, at the instant a switch is closed in a circuit, the current finds a minimum of opposition and starts to flow. However, the change in current flow from zero to maximum induces a maximum EMF that opposes the current flow. ![[Pasted image 20210808180643.png|350]] This means that when plotted against each other, the voltage will rise and then subsequently the current will rise. We refer to this as the voltage leading the current. We will see more of this in the coming weeks, but to remember that voltage leads current in an inductive circuit, you can refer to ELI the ICE man. Ignoring the ICE part for now, E leads I in an inductive circuit: E _L_ I ### Time Constant of Inductors Because the voltage leads the current, current does not begin to flow at its maximum rate instantly. The time required for the current to rise to 63.2% of its peak value is known as the time constant of the circuit. The TC is determined by the value of inductance and the resistance in the circuit. ![[Pasted image 20210808180712.png|350]] You may be wondering where the numbers 86%, 95% and 99% come from. Take out your calculator and consider that for each time constant there is a 63.2% increase. So, after the first time constant, there would remain 36.8% until max current. 63.2% of that is 23.3, so after two time constants, we have reached 63.2 plus 23.3 percent of max current, which equals 86.5% (roughly). See if the following numbers in the graph make similar sense. #### Time Constant Example A circuit contains 2 Henrys of inductance and 50 ohms of resistance. This circuit has a time constant of 0.04 seconds (40 milliseconds). ![[Pasted image 20210808180800.png|350]] Therefore, the current rises to 63.2 % of its peak value in a period of time equal to one time constant (0.04 seconds). In two time constants, or 0.08 seconds, the current rises to 86.5 % of its peak value. Remember that this is 63.2% of the remaining max that is added to the first 63.2% that occurred in the first time constant. In three time constants (0.12 seconds) it rises to 95%. In four time constants (0.16 seconds) it rises to 98%. It takes five time constants, or 0.2 seconds, for the current to reach the peak value of the source. Note here that in actual fact, we are increasing by 63.2% (our TC) every second, so effectively, we are increasing by the same [[percentage]] for every TC, but the actual values become very small indeed. For those of you who are sticklers for detail, notice that in the diagram above, the fraction of the max at 5TC is 99%. ![[Pasted image 20210808180903.png|350]] And it will behave the same way when the current source is turned off. When the current decreases rapidly, the counter EMF kicks in, and the process is slowed as the current is affected by this opposing induced voltage. # Lab This week in the lab, we will conduct MP 105-1. You can see an example [[MP105 1|here]]. It is a calculation and measurement exercise much like we went through [[T105 Week 6#Circuit Analysis of a Series Parallel Circuit|here]]. [[MP105 1.pdf|Pdf version]] You can see a complete walkthrough of both types of circuits for the MP [here](https://vimeo.com/1129308362/aa2facf096?fl=ip&fe=ec "https://vimeo.com/1129308362/aa2facf096?fl=ip&fe=ec") [[T105L SAFETY|Safety Briefing]]