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- 1. 5 This month Paul Coxwell examines the concept oíInductance 18 RackToBasics ----......----- Fig.1 The magnetic field around a coil A t this point in the series you should have a good knowledge of basic electrical circuits. Back in part 2 we examined the link between magnetism and electricity, and saw that a magnetic field is gener- ated around a current-carrying conductor. The existence of this field can be proven by placing a small compass next to the conductor. The electromagnet is a device which puts this field to good use. If a wire is wound into a coil, the magnetic field surrounding each turn of the conductor combines with those next to it. This results in a much stronger magnetic field surrounding the coil (Figure. 1). The magnetic field may be strengthened by increasing the current flowing through the coil or by adding extra turns to the coil. The amount of magnetic power available is called the magneto-motive force (MMF) and is measured in ampere-turns. For example, if a current of 2A is passed through a 10-turn coil of wire, the MMF is 20 ampere-turns. The same MMF could also be obtained by passing lA through a 10-turn coil, or 0.5A through a 40-turn coil. Air is (l CDRE---.. COIL ARROWS INDICATE THE MOVEMENT Of ARMATURE WHEN RELAY IS ENERGISED Fig.2 The Relay not one of the best conductors of magnetic lines of flux, and practical electromagnets are wound with a soft iron core. This core concentrates the magnetic field and the resulting electromagnet can be used in a variety of applications. One application is that of the relay (Figure 2) . A relay can be thought of as a remote switch;jnstead of a small lever being used to open or close the switch contacts, an electromagnet is employed instead. When a current is passed through the coil it generates a magnetic field. This field causes the relay's armature to be pulled clown, thus activating the contacts. Relays are available in many different sizes, from miniature types intended for remote-control of models right up to industrial power relays that are capable of switching very powerful equipment on and off. The relay allows current flow in one circuit to control another, without there being any direct electrical connection between the two. lt is, for instance, a common requirement to be able to remotely control a very large electric motor. The cables that supply power to the motor may need to be very thick in order to carry the high current; to run such cables over severa! hundred yards would be impractical, not to mention very expensive.If a relay is fitted at the motor site, however, much lighter wires can be used to connect to the relay' s coil to provide remote control. Figure 3 shows another way in which electromagnets Fig.3 The Electric Bell are used: a common electric bell. Notice that the bell also has a pair of contacts, just like the relay, only this time they form part of the circuit to the coils themselves. When power is applied, the coils generate a magnetic field which attracts the armature, causing it to strike the bell gong. At the same time, the movement of the armature has opened the switch contacts, thus removing power to the coils. A spring returns the armature to its former position, which doses the contacts and applies power to the coils once again. The whole process is repeated several times a second, with the result that the gong is repeatedly hit to produce a continuous ringing sound. The relay and the electric bell are just two examples of the way in which a coil may be used to control externa! events by way of the generated magnetic field. There is another important aspect of the coil, however, in that it can influence the circuit of which it forms a part. This property is called inductance. lnductance Recall that when a conductor is moved across a magnetic field (or vice versa), a current is induced. This is the converse relationship to a current causing a magnetic field to be generated. Thinking carefully about the construction of a coil (Figure 4) , as current through the coil increases, a magnetic field is formed around each loop of the coil. As this field expands, it cuts across neighboring turns of the coi!, and induces ETI JUNE 1991
- 2. a current in those turns. Each turn of wire forms part of the same conductor, so the induced current will either aid or oppose that already flowing depending on whether the field is rising orfalling. This action is known as self-inductance. Application of the Left and Right-hand Rules shows that the induced current opposes the original current, and the induced voltage is called a counter- EMF, because it istryingto counteractthe applied EMF lt is importantto rememberthatthis self-induction takes place only when the current through the coi! is changing;when the currentreaches a constantleve1the magnetic field around each loop stops expanding, so there is no relative movement between the field and neighbouring loops. A coi! not only opposes any increase in current - italso opposes any decrease in current. As the supply currentdecreases, the magneticfield around each loop ofthe coi!startsto collapse, cutting across neighboring EXPAlllOING MAGNETIC LllllES OF FLUX CUT ACROSS lllEJGHBOURING TURlllS Of THE COIL Fig.4 Self lnductance in a coil loops as it does so. Self induction takes place once again, but this time the induced EMF aids the applied EMF , so the coi! tries to keep the current from decreasing. Figure 5 shows the action of a coi!, or inductor, in a simple circuit. The first diagram shows a circuit which should now be familiar: a battery, switch, and load resistor. When the switch is operated, current through the resistor rises almost instantaneously to a value determined by Ohm's Law, as shown in the graph. When the switch is moved back to its original position, current stops flowing straight away - the power source has been removed and a resistor has no way to store power. The second part of the diagram shows how the circuit responds when an inductor (coi!) is used. When the battery is connected to the resistor and coi!, current starts to flow. As this current builds up, self-induction in the coi! tends to oppose the flow of current. The counter-EMF generated is not strong enough to stop the increase in current, but it does slow it clown considerably. The result is that current increases much more slowly than it did in the purely resistive circuit. Current is limited to a specifíc value by the resistor, and once it reaches that leve! self- induction ceases. Note the way in which the current increases: quickly at first and then more slowly. When the switch is moved to its other position power from the battery is removed and the resistor is connected as a load across the coi!. Self-induction causes the coil to oppose the decrease in current, with the result that current drops gradually rather than instantaneously. As with any other electrical property, it is necessary to be able to specify how much effect a given coil will have upon a circuit, and the unit for measuring inductance is the Henry. There are two new symbols to remember: 'l.'. for inductance (it is also used to label coils on schematic diagrams) and 'H' for Henry. The definition of the Henry is that it is the amount of inductance which will cause an EMF of lV to be induced when the current changes at a rate of ETI JUNE 1991 R R 1 n Fig.5 lnductance in a OC circuit o 1 1 SWITCH OPEAATEO 1 SWITCH MOVED TO POSITION 1 lA persecond. ln other words, a lH coil will generate its own EMF of lVifthe supply current changes from, say, ZA to 3A in one second. The value of the induced EMF is not often required for most work, however, anda more useful measurement is that known as the time constan! of a circuit. The time constan! is the period of time it takes for the current to increase to 63.2% of its maximum value. In Figure 6, the maximum current value is calculated using Ohm's Law - the result is lOOmA. The amount of time taken between the closure of the switch and the currentreaching a leve! of63.ZmA (i e 63.2% of lOOmA) is the time constant. The time constant can be calculated by way of a simple formula which states that the time is directly proportional to the inductance and inversely proportional to the resistance in the circuit The time constant can be lengthened by increasing the induct- 100 75 63 2roA-- ,_ 50 ~ a: :> u 25 o .l 10V --=-- 1 - FROM OHM'S LAW: R 100R 1 = E/R = 10V/100R = 100mA TIME CONSTANT. t = L/R so 11 L lOli t = L/R = 10H/100A = O1 SECOND Fig.6 Time constant in an LR circuit TIME SWITCH MOVED TO POSITION 2 19
- 3. 20 +16 p -10 ~~-,-~~-.-~~.....-~-..~~-.-~---,.....-~-..~--. o 46 90 135 180 226 270 315 360 DEGREES 1 - ·O· CURRENT AND VOLTAGE IN PHASE Fig.7 Resistive AC circuit ... 10 so• p anee or reducing the resistance. Notice that the time constant is affected by the entire circuit, not just the coi! itself. In the circuit shown, the current through the coi! will reach 63.2% of its maximum value in one- tenth of a second. The measurement of the time constant also applies when current through the coil is decreasing. lt is the period of time it takes for the curren! to CURRENT LAGS VOLTAGE BY 90° VOLTAGE LEADS CURRENT BY 90° AVERAGE POWER ~ O - IOL-~--,..~~-.-~~r-~--,..~~-.-~~r-~-,-~--, O 45 90 135 180 225 Z70 315 380 DEGREES Fig.8 lnductive AC circuit diminish by 63.2% of its original value (or, to put it another way, the length of time it takes for the current to drop to 36.8% of its starting value). We have covered sorne importan! concepts in the preceding section, so it is worth pausing for a moment to recapitulate. Here are the importan! points to remember: Inductance always opposes a change in curren!; increasing supply curren! causes self- induction to generate a counter-EMF; decreasing su¡:íply curren! causes self-induction to generate an aiding EMF; an inductor stores energy in the form of a magnetic field. lnductance In AC Circuits So far we have seen how inductance affects OC circuits by delaying the build-up of curren! to its maximum value. In an AC circuí!, the situation becomes a little more complex. Figure 7 shows a simple AC circuí! consisting of just one load resistor anda power source. The graph should look familiar - it is the one we used last month to examine power in AC circuits. Notice how the voltage and curren! curves, E and 1, are in phase with each other (i.e. they both reach their positive peak at the same time, both cross the zero point at the same time, and so on) . Recall that the power curve never goes negative, because the product of two negative values (E and 1) is always a positive value. In Figure 8 the resistor has been replaced by an inductor. Look closely at the voltage and curren!curves and you will see thatthey are 90° out of phase - as E reaches its negative peak,for instance, 1is just crossing zero on its way to the negative peak. We can say either that the curren! lags the voltage by 90° or that the voltage leads the curren! by 90°.The descriptions are equivalen! and are justtwo different ways ofsayingthe same thing. The reason for this phase shift is the self- inductance ofthe coil. The phase ofthe source voltage is determined by the power supply, but the inductor causes the current to lag behind. The graph in Figure 8 also shows how the power curve would appear. When voltage and curren! are both positive or both negative, the resulting product (P) is positive. When either E or 1is positive and the other is negative, the power curve drops below zero. As has been already stated, a negative power levelimplies that the circuí! is supplying power instead of consuming it. During the positive parts ofthe powercyclethe inductoriscreating an expanding magnetic field. During the negative portions, the magnetic field is collapsing and returning its energy to the circuí!. You will see that the power curve is symmetrical and centered on zero, so its average level is, therefore, zero. This leads to an importan! fact: A purely inductive circuit, such as the one shown, does no! consume any power. Ali the power taken to create a ETI JUNE 1991
- 4. OHM'S LAW FOR REACTANCE: 1 = E/X THEREFORE E = IX ANO X = E/I X = REACTANCE XL = INDUCTIVE REACTANCE XL = 2rrfL WHERE L = INDUCTANCE. f = FREQUENCY EXAMPLE: XL = 2nfl 1 - = 2 X 3.14 X 60 X 2 =~ XL =? l = , L 2H 1 = E/XL = 120V/753 6R = 159mA Fig.9 lnductive Reactance magnetic field around the coi! is returned when the field collapses. Inductance opposes the flow of alternating current but not direct current. In a DC circuit the current will eventually build up to its maximum value, but in an AC circuit the polarity of the supply voltage has changed before the curren! has had time to reach that same leve!. The inductor may be considered to have a special kind of 'resistance' to alternating current only. To avoid confusion, this opposition to the flow of AC is called reactance, and when applied to coils it is called inductive reactance (you will come across another type of reactance Jater in this series). Reactance is not constan! for any particular coi! - it varíes with the frequency of the alternating current. lf the frequency of the AC supply is increased, the curren! does not have as much time to increase before the supply voltage changes polarity. The result is that current decreases as frequency increases, orto put it more formally, inductive reactance is directly proportional to frequency. The inductance value of the coi! itself also affects the amount of reactance; more inductance gives a longer time constan! for the circuit, thereby preventing curren! from increasing so rapidly. lnductive reactance, therefore, is also directly proportional to inductance. The symbolfor reactance is 'X' and when referring to inductivereactance itis usual to addthe subscript 'l.: to avoid confusion. Like resistance, reactance is measured in ohms, and the formula for calculating inductive reactance is shown in Figure 9. For most practica) purposes it is accurate enough to take rr as 3.14. The example shows a 2H inductor connected directly across'"a 120V 60Hz supply. Applying the formula for XL gives an inductive reactance of 753.6 ohms. Although Ohm's Law is stated in terms of curren!, voltage, and resistance, it may also be applied to current, voltage, and reactance. The curren!flowing in the circuit may be calculated by dividing the reactance into the supply voltage. The result is a curren! of approximately 159mA. One may be tempted to multiply the supply voltage and current together in order to calculate the power dissipation - doing so gives aresult ofjusiover 19 watts. We have alreadyseen that an inductive circuit does not in theory consume any power. The explanation ofthis problem forms the basis of next month's installment. and pages 45, 55, 58 among others Simply that these are sorne of the pages whlch show how exceptionally wide and varled are the ranges of COMPONENTS, PRODUCTSand MATERIALStobefound in our 1991 Catalogue. Much practica! information is included and it's ali well presented, illustrated and easy to look up - and to order from. WE ARE SPECIALIST SUPPLIERS FOR SIEMENS FINEQUALITY COMPONENTS Please send f1SO (cash/P.O.loheque/stamps) for your 1991 EV catalogue (postage paid In UK) We give you a refund voucherfor f1.50 usable towards your next order for E:5.00 or more. FOR QUALITY COMPONENTS COMPETITIVELY PRICED Catalogue orders to:- ELECTROVALUE LTD, 28a ST. Jude's Ad., Englefield Green, Egham, SurreyTW20 OHB Phone: 0784 433 603 Fax: 0784 435 216 ETI JUNE 1991 21