Magnetic circuits. Chapter Introduction to magnetism and magnetic circuits. At the end of this chapter you should be able to:

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1 Chapter 7 Magnetic circuits At the end of this chapter you shoud be abe to: appreciate some appications of magnets describe the magnetic fied around a permanent magnet state the aws of magnetic attraction and repusion for two magnets in cose proximity define magnetic fux,, and magnetic fux density, B, and state their units perform simpe cacuations invoving B /A define magnetomotive force, F m, and magnetic fied strength, H, and state their units perform simpe cacuations invoving F m NI and H NI/ define permeabiity, distinguishing between µ 0, µ r and µ understand the B H curves for different magnetic materias appreciate typica vaues of µ r perform cacuations invoving B µ 0 µ r H define reuctance, S, and state its units perform cacuations invoving S m.m.f. µ 0 µ r A perform cacuations on composite series magnetic circuits compare eectrica and magnetic quantities appreciate how a hysteresis oop is obtained and that hysteresis oss is proportiona to its area 7.1 Introduction to magnetism and magnetic circuits The study of magnetism began in the thirteenth century with many eminent scientists and physicists such as Wiiam Gibert, Hans Christian Oersted, Michae Faraday, James Maxwe, André Ampère and Wihem Weber a having some input on the subject since. The association between eectricity and magnetism is a fairy recent finding in comparison with the very first understanding of basic magnetism. Today, magnets have many varied practica appications. For exampe, they are used in motors and generators, teephones, reays, oudspeakers, computer hard drives and foppy disks, anti-ock brakes, cameras, fishing rees, eectronic ignition systems, keyboards, t.v. and radio components and in transmission equipment.

2 72 Eectrica and Eectronic Principes and Technoogy The fu theory of magnetism is one of the most compex of subjects; this chapter provides an introduction to the topic. 7.2 Magnetic fieds A permanent magnet is a piece of ferromagnetic materia (such as iron, nicke or cobat) which has properties of attracting other pieces of these materias. A permanent magnet wi position itsef in a north and south direction when freey suspended. The north-seeking end of the magnet is caed the north poe, N, and the south-seeking end the south poe, S. The area around a magnet is caed the magnetic fied and it is in this area that the effects of the magnetic force produced by the magnet can be detected. A magnetic fied cannot be seen, fet, smet or heard and therefore is difficut to represent. Michae Faraday suggested that the magnetic fied coud be represented pictoriay, by imagining the fied to consist of ines of magnetic fux, which enabes investigation of the distribution and density of the fied to be carried out. The distribution of a magnetic fied can be investigated by using some iron fiings. A bar magnet is paced on a fat surface covered by, say, cardboard, upon which is sprinked some iron fiings. If the cardboard is genty tapped the fiings wi assume a pattern simiar to that shown in Fig If a number of magnets of different strength are used, it is found that the stronger the fied the coser are the ines of magnetic fux and vice versa. Thus a magnetic fied has the property of exerting a force, demonstrated in this case by causing the iron fiings to move into the pattern shown. The strength of the magnetic fied decreases as we move away from the magnet. It shoud be reaized, of course, that the magnetic fied is three dimensiona in its effect, and not acting in one pane as appears to be the case in this experiment. If a compass is paced in the magnetic fied in various positions, the direction of the ines of fux may be determined by noting the direction of the compass pointer. The direction of a magnetic fied at any point is taken as that in which the north-seeking poe of a compass neede points when suspended in the fied. The direction of a ine of fux is from the north poe to the south poe on the outside of the magnet and is then assumed to continue through the magnet back to the point at which it emerged at the north poe. Thus such ines of fux aways form compete cosed oops or paths, they never intersect and aways have a definite direction. The aws of magnetic attraction and repusion can be demonstrated by using two bar magnets. In Fig. 7.2(a), with unike poes adjacent, attraction takes pace. Lines of fux are imagined to contract and the magnets try to pu together. The magnetic fied is strongest in between the two magnets, shown by the ines of fux being cose together. In Fig. 7.2(b), with simiar poes adjacent (i.e. two north poes), repusion occurs, i.e. the two north poes try to push each other apart, since magnetic fux ines running side by side in the same direction repe. Figure Magnetic fux and fux density Figure 7.1 Magnetic fux is the amount of magnetic fied (or the number of ines of force) produced by a magnetic source. The symbo for magnetic fux is (Greek etter phi ). The unit of magnetic fux is the weber, Wb. Magnetic fux density is the amount of fux passing through a defined area that is perpendicuar to the direction of the fux: magnetic fux Magnetic fux density area

3 Magnetic circuits 73 The symbo for magnetic fux density is B. The unit of magnetic fux density is the tesa, T, where 1 T 1 Wb/m 2. Hence where A(m 2 ) is the area B A tesa Magnetic fied strength (or magnetising force), H NI ampere per metre where is the mean ength of the fux path in metres. Thus m.m.f. NI H amperes Probem 1. A magnetic poe face has a rectanguar section having dimensions 200 mm by 100 mm. If the tota fux emerging from the poe is 150 µwb, cacuate the fux density. Fux 150 µwb Wb Cross sectiona area A mm m 2. Fux density, B A T or 7.5 mt Probem 2. The maximum working fux density of a ifting eectromagnet is 1.8 T and the effective area of a poe face is circuar in cross-section. If the tota magnetic fux produced is 353 mwb, determine the radius of the poe face. Fux density B 1.8 T and fux 353 mwb Wb. Since B /A, cross-sectiona area A /B i.e. A m m 2 The poe face is circuar, hence area πr 2, where r is the radius. Hence πr from which, r /π and radius r (0.1961/π) m i.e. the radius of the poe face is 250 mm. 7.4 Magnetomotive force and magnetic fied strength Magnetomotive force (m.m.f.) is the cause of the existence of a magnetic fux in a magnetic circuit, m.m.f. F m NI amperes where N is the number of conductors (or turns) and I is the current in amperes. The unit of m.m.f is sometimes expressed as ampere-turns. However since turns have no dimensions, the S.I. unit of m.m.f. is the ampere. Probem 3. A magnetising force of 8000A/m is appied to a circuar magnetic circuit of mean diameter 30 cm by passing a current through a coi wound on the circuit. If the coi is uniformy wound around the circuit and has 750 turns, find the current in the coi. H 8000A/m, πd π m and N 750 turns. Since H NI/, then I H N Thus, current I A 8000 π Now try the foowing exercise Exercise 32 Further probems on magnetic circuits 1. What is the fux density in a magnetic fied of cross-sectiona area 20 cm 2 having a fux of 3 mwb? [1.5 T] 2. Determine the tota fux emerging from a magnetic poe face having dimensions 5 cm by 6 cm, if the fux density is 0.9 T [2.7 mwb] 3. The maximum working fux density of a ifting eectromagnet is 1.9 T and the effective area of a poe face is circuar in cross-section. If the tota magnetic fux produced is 611 mwb determine the radius of the poe face. [32 cm] 4. A current of 5A is passed through a 1000-turn coi wound on a circuar magnetic circuit of radius 120 mm. Cacuate (a) the magnetomotive force, and (b) the magnetic fied strength. [(a) 5000A (b) 6631A/m] 5. An eectromagnet of square cross-section produces a fux density of 0.45 T. If the magnetic

4 74 Eectrica and Eectronic Principes and Technoogy fux is 720 µwb find the dimensions of the eectromagnet cross-section. [4 cm by 4 cm] 6. Find the magnetic fied strength appied to a magnetic circuit of mean ength 50 cm when a coi of 400 turns is appied to it carrying a current of 1.2A [960A/m] 7. A soenoid 20 cm ong is wound with 500 turns of wire. Find the current required to estabish a magnetising force of 2500 A/m inside the soenoid. [1A] 8. A magnetic fied strength of 5000 A/m is appied to a circuar magnetic circuit of mean diameter 250 mm. If the coi has 500 turns find the current in the coi. [7.85A] 7.5 Permeabiity and B H curves For air, or any non-magnetic medium, the ratio of magnetic fux density to magnetising force is a constant, i.e. B/H a constant. This constant is µ 0, the permeabiity of free space (or the magnetic space constant) and is equa to 4π 10 7 H/m, i.e. for air, or any non-magnetic medium, the ratio B H µ 0 (Athough a non-magnetic materias, incuding air, exhibit sight magnetic properties, these can effectivey be negected.) For a media other than free space, B H µ 0µ r where µ r is the reative permeabiity, and is defined as µ r fux density in materia fux density in a vacuum µ r varies with the type of magnetic materia and, since it is a ratio of fux densities, it has no unit. From its definition, µ r for a vacuum is 1. µ 0 µ r µ, caed the absoute permeabiity By potting measured vaues of fux density B against magnetic fied strength H, a magnetisation curve (or B H curve) is produced. For non-magnetic materias this is a straight ine. Typica curves for four magnetic materias are shown in Fig. 7.3 Figure 7.3 The reative permeabiity of a ferromagnetic materia is proportiona to the sope of the B H curve and thus varies with the magnetic fied strength. The approximate range of vaues of reative permeabiity µ r for some common magnetic materias are: Cast iron µ r Mid stee µ r Siicon iron µ r Cast stee µ r Mumeta µ r Staoy µ r Probem 4. A fux density of 1.2 T is produced in a piece of cast stee by a magnetising force of 1250A/m. Find the reative permeabiity of the stee under these conditions. For a magnetic materia: B µ 0 µ r H i.e. µ r B µ 0 H 1.2 (4π 10 7 )(1250) 764 Probem 5. Determine the magnetic fied strength and the m.m.f. required to produce a fux density of 0.25 T in an air gap of ength 12 mm.

5 Magnetic circuits 75 For air: B µ 0 H (since µ r 1) Magnetic fied strength, H B A/m µ 0 4π 10 7 m.m.f. H A (a) (b) H NI π A/m B µ 0 µ r H, hence µ r B µ 0 H 0.4 (4π 10 7 )(1592) 200 Probem 6. A coi of 300 turns is wound uniformy on a ring of non-magnetic materia. The ring has a mean circumference of 40 cm and a uniform cross-sectiona area of 4 cm 2. If the current in the coi is 5A, cacuate (a) the magnetic fied strength, (b) the fux density and (c) the tota magnetic fux in the ring. (a) (b) Magnetic fied strength H NI A/m For a non-magnetic materia µ r 1, thus fux density B µ 0 H i.e B 4π mt (c) Fux BA ( )( ) µwb Probem 7. An iron ring of mean diameter 10 cm is uniformy wound with 2000 turns of wire. When a current of 0.25A is passed through the coi a fux density of 0.4 T is set up in the iron. Find (a) the magnetising force and (b) the reative permeabiity of the iron under these conditions. πd π 10 cm π m, N 2000 turns, I 0.25A and B 0.4T Probem 8. A uniform ring of cast iron has a cross-sectiona area of 10 cm 2 and a mean circumference of 20 cm. Determine the m.m.f. necessary to produce a fux of 0.3 mwb in the ring. The magnetisation curve for cast iron is shown on page 74. A 10 cm m 2, 20 cm 0.2 m and Wb. Fux density B T A From the magnetisation curve for cast iron on page 74, when B 0.3 T, H 1000 A/m, hence m.m.f. H A A tabuar method coud have been used in this probem. Such a soution is shown beow in Tabe 7.1. Probem 9. From the magnetisation curve for cast iron, shown on page 74, derive the curve of µ r against H. B µ 0 µ r H, hence µ r B µ 0 H 1 µ 0 B H 107 4π B H A number of co-ordinates are seected from the B H curve and µ r is cacuated for each as shown in Tabe 7.2. µ r is potted against H as shown in Fig The curve demonstrates the change that occurs in the reative permeabiity as the magnetising force increases. Tabe 7.1 Part of Materia (Wb) A(m 2 ) B (T) H from (m) m.m.f. A circuit graph H(A) Ring Cast iron

6 76 Eectrica and Eectronic Principes and Technoogy Tabe 7.2 B(T) H(A/m) µ r 107 4π B H m r B Figure H (A/m) Now try the foowing exercise m r B Exercise 33 Further probems on magnetic circuits (Where appropriate, assume µ 0 4π 10 7 H/m) 1. Find the magnetic fied strength and the magnetomotive force needed to produce a fux density of 0.33 T in an air-gap of ength 15 mm. [(a) A/m (b) 3939A] 2. An air-gap between two poe pieces is 20 mm in ength and the area of the fux path across the gapis5cm 2. If the fux required in the air-gap is 0.75 mwb find the m.m.f. necessary. [23 870A] 3. (a) Determine the fux density produced in an air-cored soenoid due to a uniform magnetic fied strength of 8000A/m (b) Iron having a reative permeabiity of 150 at 8000 A/m is inserted into the soenoid of part (a). Find the fux density now in the soenoid. [(a) mt (b) T] 4. Find the reative permeabiity of a materia if the absoute permeabiity is H/m. [325] 5. Find the reative permeabiity of a piece of siicon iron if a fux density of 1.3 T is produced by a magnetic fied strength of 700A/m. [1478] 6. A stee ring of mean diameter 120 mm is uniformy wound with 1500 turns of wire. When a current of 0.30A is passed through the coi a fux density of 1.5 T is set up in the stee. Find the reative permeabiity of the stee under these conditions. [1000] 7. A uniform ring of cast stee has a crosssectiona area of 5 cm 2 and a mean circumference of 15 cm. Find the current required in a coi of 1200 turns wound on the ring to produce a fux of 0.8 mwb. (Use the magnetisation curve for cast stee shown on page 74) [0.60 A] 8. (a) A uniform mid stee ring has a diameter of 50 mm and a cross-sectiona area of 1 cm 2. Determine the m.m.f. necessary to produce a fux of 50 µwb in the ring. (Use the B H curve for mid stee shown on page 74) (b) If a coi of 440 turns is wound uniformy around the ring in Part (a) what current woud be required to produce the fux? [(a) 110A (b) 0.25A] 9. From the magnetisation curve for mid stee shown on page 74, derive the curve of reative permeabiity against magnetic fied strength. From your graph determine (a) the vaue of µ r when the magnetic fied strength is 1200 A/m, and (b) the vaue of the magnetic fied strength when µ r is 500. [(a) (b) 2000]

7 Magnetic circuits Reuctance Reuctance S (or R M ) is the magnetic resistance of a magnetic circuit to the presence of magnetic fux. Reuctance, S F M NI H BA (B/H)A µ 0 µ r A The unit of reuctance is 1/H (or H 1 ) or A/Wb. Ferromagnetic materias have a ow reuctance and can be used as magnetic screens to prevent magnetic fieds affecting materias within the screen. Probem 10. Determine the reuctance of a piece of mumeta of ength 150 mm and cross-sectiona area 1800 mm 2 when the reative permeabiity is Find aso the absoute permeabiity of the mumeta. Reuctance, S µ 0 µ r A (4π 10 7 )(4000)( ) /H Absoute permeabiity, µ µ 0 µ r (4π 10 7 )(4000) H/m (b) S m.m.f. from which m.m.f. S i.e. NI S Hence, number of terms N S I Now try the foowing exercise turns Exercise 34 Further probems on magnetic circuits (Where appropriate, assume µ 0 π 10 7 H/m) 1. Part of a magnetic circuit is made from stee of ength 120 mm, cross sectiona area 15 cm 2 and reative permeabiity 800. Cacuate (a) the reuctance and (b) the absoute permeabiity of the stee. [(a) /H (b) 1 mh/m] 2. A mid stee cosed magnetic circuit has a mean ength of 75 mm and a cross-sectiona area of mm 2. A current of 0.40A fows in a coi wound uniformy around the circuit and the fux produced is 200 µwb. If the reative permeabiity of the stee at this vaue of current is 400 find (a) the reuctance of the materia and (b) the number of turns of the coi. [(a) /H (b) 233] Probem 11. A mid stee ring has a radius of 50 mm and a cross-sectiona area of 400 mm 2.A current of 0.5A fows in a coi wound uniformy around the ring and the fux produced is 0.1 mwb. If the reative permeabiity at this vaue of current is 200 find (a) the reuctance of the mid stee and (b) the number of turns on the coi. 2πr 2 π m, A m 2, I 0.5A, Wb and µ r 200 (a) Reuctance, S µ 0 µ r A 2 π (4π 10 7 )(200)( ) /H 7.7 Composite series magnetic circuits For a series magnetic circuit having n parts, the tota reuctance S is given by: S S 1 + S S n (This is simiar to resistors connected in series in an eectrica circuit). Probem 12. A cosed magnetic circuit of cast stee contains a 6 cm ong path of cross-sectiona area 1 cm 2 and a 2 cm path of cross-sectiona area 0.5 cm 2. A coi of 200 turns is wound around the 6 cm ength of the circuit and a current of 0.4A fows. Determine the fux density in the 2 cm path, if the reative permeabiity of the cast stee is 750.

8 78 Eectrica and Eectronic Principes and Technoogy For the 6 cm ong path: Reuctance S 1 1 µ 0 µ r A (4π 10 7 )(750)( ) /H From the B H curve for siicon iron on page 74, when B 1.4 T, H 1650A/m. Hence the m.m.f. for the iron path H A For the air gap: The fux density wi be the same in the air gap as in the iron, i.e. 1.4 T (This assumes no eakage or fringing occurring). For air, For the 2 cm ong path: Reuctance S 2 2 µ 0 µ r A (4π 10 7 )(750)( ) /H Tota circuit reuctance S S 1 + S 2 S m.m.f. ( ) /H m.m.f. i.e. NI S S Wb Fux density in the 2 cm path, H B µ A/m 4π 10 7 Hence the m.m.f. for the air gap H A. Tota m.m.f. to produce a fux of 0.6 mwb A. A tabuar method coud have been used as shown in Tabe 7.3 at top of next page. Probem 14. Figure 7.5 shows a ring formed with two different materias cast stee and mid stee. B A T Probem 13. A siicon iron ring of cross-sectiona area 5 cm 2 has a radia air gap of 2 mm cut into it. If the mean ength of the siicon iron path is 40 cm cacuate the magnetomotive force to produce a fux of 0.7 mwb. The magnetisation curve for siicon is shown on page 74. Figure 7.5 The dimensions are: mean ength cross-sectiona area There are two parts to the circuit the siicon iron and the air gap. The tota m.m.f. wi be the sum of the m.m.f. s of each part. Mid stee 400 mm 500 mm 2 Cast stee 300 mm mm 2 For the siicon iron: B A T Find the tota m.m.f. required to cause a fux of 500 µwb in the magnetic circuit. Determine aso the tota circuit reuctance.

9 Magnetic circuits 79 Tabe 7.3 Part of Materia (Wb) A(m 2 ) B(T) H(A/m) (m) m.m.f. circuit H(A) Ring Siicon iorn (from graph) Air-gap Air π Tota: 2888 A Tabe 7.4 Part of Materia (Wb) A(m 2 ) B(T) H(A/m) (from (m) m.m.f. circuit ( /A) graphs page 74) H(A) A Mid stee B Cast stee Tota: 2000 A A tabuar soution is shown in Tabe 7.4 above. } Tota circuit S m.m.f. reuctance /H Probem 15. A section through a magnetic circuit of uniform cross-sectiona area 2 cm 2 is shown in Fig The cast stee core has a mean ength of 25 cm. The air gap is 1 mm wide and the coi has 5000 turns. The B H curve for cast stee is shown on page 74. Determine the current in the coi to produce a fux density of 0.80 T in the air gap, assuming that a the fux passes through both parts of the magnetic circuit. Reuctance of core S 1 1 µ 0 µ r A 1 and since B µ 0 µ r H, then µ r S 1 For the air gap: 1 ( ) B µ 0 A 1 µ 0 H ( )(750) (0.8)( ) 2 Reuctance, S 2 µ 0 µ r A 2 B µ 0 H. 1 H BA /H 2 µ 0 A 2 (since µ r 1 for air) (4π 10 7 )( ) /H Tota circuit reuctance Figure 7.6 For the cast stee core, when B 0.80 T, H 750A/m (from page 74). S S 1 + S /H Fux BA Wb

10 80 Eectrica and Eectronic Principes and Technoogy thus S m.m.f. m.m.f. S hence NI S iron magnetic circuit has a uniform crosssectiona area of 3 cm 2 and its magnetisation curve is as shown on page 74. [0.83A] and current I S N ( )( ) A Now try the foowing exercise Exercise 35 Further probems on composite series magnetic circuits 1. A magnetic circuit of cross-sectiona area 0.4cm 2 consists of one part 3 cm ong, of materia having reative permeabiity 1200, and a second part 2 cm ong of materia having reative permeabiity 750. With a 100 turn coi carrying 2A, find the vaue of fux existing in the circuit. [0.195 mwb] 2. (a) A cast stee ring has a cross-sectiona area of 600 mm 2 and a radius of 25 mm. Determine the m.m.f. necessary to estabish a fux of 0.8 mwb in the ring. Use the B H curve for cast stee shown on page 74. (b) If a radia air gap 1.5 mm wide is cut in the ring of part (a) find the m.m.f. now necessary to maintain the same fux in the ring. [(a) 270A (b)1860a] Figure A ring forming a magnetic circuit is made from two materias; one part is mid stee of mean ength 25 cm and cross-sectiona area 4 cm 2, and the remainder is cast iron of mean ength 20 cm and cross-sectiona area 7.5 cm 2. Use a tabuar approach to determine the tota m.m.f. required to cause a fux of 0.30 mwb in the magnetic circuit. Find aso the tota reuctance of the circuit. Use the magnetisation curves shown on page 74. [550A, /H] 6. Figure 7.8 shows the magnetic circuit of a reay. When each of the air gaps are 1.5 mm wide find the m.m.f. required to produce a fux density of 0.75 T in the air gaps. Use the B H curves shown on page 74. [2970A] 3. A cosed magnetic circuit made of siicon iron consists of a 40 mm ong path of crosssectiona area 90 mm 2 and a 15 mm ong path of cross-sectiona area 70 mm 2. A coi of 50 turns is wound around the 40 mm ength of the circuit and a current of 0.39A fows. Find the fux density in the 15 mm ength path if the reative permeabiity of the siicon iron at this vaue of magnetising force is [1.59 T] 4. For the magnetic circuit shown in Fig. 7.7 find the current I in the coi needed to produce a fux of 0.45 mwb in the air-gap. The siicon Figure 7.8

11 Magnetic circuits Comparison between eectrica and magnetic quantities Eectrica circuit e.m.f. E (V) current I (A) Magnetic circuit m.m.f. F m (A) fux (Wb) resistance R ( ) reuctance S (H 1 ) I E R R ρ A m.m.f. S S µ 0 µ r A 7.9 Hysteresis and hysteresis oss Hysteresis oop Let a ferromagnetic materia which is competey demagnetised, i.e. one in which B H 0 be subjected to increasing vaues of magnetic fied strength H and the corresponding fux density B measured. The resuting reationship between B and H is shown by the curve Oab in Fig At a particuar vaue of H, shown as Oy, it becomes difficut to increase the fux density any further. The materia is said to be saturated. Thus by is the saturation fux density. If the vaue of H is now reduced it is found that the fux density foows curve bc. When H is reduced to zero, fux remains in the iron. This remanent fux density or remanence is shown as Oc in Fig When H is increased in the opposite direction, the fux density decreases unti, at a vaue shown as Od, the fux density has been reduced to zero. The magnetic fied strength Od required to remove the residua magnetism, i.e. reduce B to zero, is caed the coercive force. Further increase of H in the reverse direction causes the fux density to increase in the reverse direction unti saturation is reached, as shown by curve de.ifh is varied backwards from Ox to Oy, the fux density foows the curve efgb, simiar to curve bcde. It is seen from Fig. 7.9 that the fux density changes ag behind the changes in the magnetic fied strength. This effect is caed hysteresis. The cosed figure bcdefgb is caed the hysteresis oop (or the B/H oop). Hysteresis oss A disturbance in the aignment of the domains (i.e. groups of atoms) of a ferromagnetic materia causes energy to be expended in taking it through a cyce of magnetisation. This energy appears as heat in the specimen and is caed the hysteresis oss. The energy oss associated with hysteresis is proportiona to the area of the hysteresis oop. The area of a hysteresis oop varies with the type of materia. The area, and thus the energy oss, is much greater for hard materias than for soft materias. Figure 7.10 shows typica hysteresis oops for: (a) (b) (c) hard materia, which has a high remanence Oc and a arge coercivity Od soft stee, which has a arge remanence and sma coercivity ferrite, this being a ceramic-ike magnetic substance made from oxides of iron, nicke, cobat, magnesium, auminium and mangenese; the hysteresis of ferrite is very sma. Figure 7.9 For a.c.-excited devices the hysteresis oop is repeated every cyce of aternating current. Thus a hysteresis oop with a arge area (as with hard stee) is often unsuitabe since the energy oss woud be considerabe. Siicon stee has a narrow hysteresis oop, and thus sma hysteresis oss, and is suitabe for transformer cores and rotating machine armatures.

12 82 Eectrica and Eectronic Principes and Technoogy 10. Compete the statement: fux density magnetic fied strength What is absoute permeabiity? 12. The vaue of the permeabiity of free space is What is a magnetisation curve? 14. The symbo for reuctance is...and the unit of reuctance is Make a comparison between magnetic and eectrica quantities 16. What is hysteresis? Figure 7.10 Now try the foowing exercise Exercise 36 Short answer questions on magnetic circuits 1. State six practica appications of magnets 2. What is a permanent magnet? 3. Sketch the pattern of the magnetic fied associated with a bar magnet. Mark the direction of the fied. 4. Define magnetic fux 5. The symbo for magnetic fux is...and the unit of fux is the Define magnetic fux density 7. The symbo for magnetic fux density is... and the unit of fux density is The symbo for m.m.f. is...and the unit of m.m.f. is the Another name for the magnetising force is...; its symbo is...and its unit is Draw a typica hysteresis oop and on it identify: (a) saturation fux density (b) remanence (c) coercive force 18. State the units of (a) remanence (b) coercive force 19. How is magnetic screening achieved? 20. Compete the statement: magnetic materias have a...reuctance;non-magnetic materias have a... reuctance 21. What oss is associated with hysteresis? Now try the foowing exercise Exercise 37 Muti-choice questions on magnetic circuits (Answers on page 398) 1. The unit of magnetic fux density is the: (a) weber (b) weber per metre (c) ampere per metre (d) tesa 2. The tota fux in the core of an eectrica machine is 20 mwb and its fux density is 1 T. The cross-sectiona area of the core is: (a) 0.05 m 2 (b) 0.02 m 2 (c) 20 m 2 (d) 50 m 2

13 Magnetic circuits If the tota fux in a magnetic circuit is 2 mwb and the cross-sectiona area of the circuit is 10 cm 2, the fux density is: (a) 0.2 T (b) 2 T (c) 20 T (d) 20 mt 10. The current fowing in a 500 turn coi wound on an iron ring is 4A. The reuctance of the circuit is H. The fux produced is: (a) 1 Wb (b) 1000 Wb (c) 1 mwb (d) 62.5 µwb Questions 4 to 8 refer to the foowing data: A coi of 100 turns is wound uniformy on a wooden ring. The ring has a mean circumference of 1 m and a uniform cross-sectiona area of 10 cm 2. The current in the coi is 1A. 4. The magnetomotive force is: (a) 1 A (b) 10 A (c) 100 A (d) 1000 A 5. The magnetic fied strength is: (a) 1 A/m (b) 10 A/m (c) 100 A/m (d) 1000 A/m 6 The magnetic fux density is: (a) 800 T (b) T (c) 4π 10 7 T (d) 40π µt 7. The magnetic fux is: (a) 0.04π µwb (b) 0.01 Wb (c) 8.85 µwb (d) 4π µwb 8. The reuctance is: 10 8 (a) 4π H 1 (b) 1000 H (c) π 109 H (d) 8.85 H 1 9. Which of the foowing statements is fase? (a) For non-magnetic materias reuctance is high (b) Energy oss due to hysteresis is greater for harder magnetic materias than for softer magnetic materias (c) The remanence of a ferrous materia is measured in ampere/metre (d) Absoute permeabiity is measured in henrys per metre 11. A comparison can be made between magnetic and eectrica quantities. From the foowing ist, match the magnetic quantities with their equivaent eectrica quantities. (a) current (b) reuctance (c) e.m.f. (d) fux (e) m.m.f. (f) resistance 12. The effect of an air gap in a magnetic circuit is to: (a) increase the reuctance (b) reduce the fux density (c) divide the fux (d) reduce the magnetomotive force 13. Two bar magnets are paced parae to each other and about 2 cm apart, such that the south poe of one magnet is adjacent to the north poe of the other. With this arrangement, the magnets wi: (a) attract each other (b) have no effect on each other (c) repe each other (d) ose their magnetism

14 Revision test 2 This revision test covers the materia contained in Chapters 5 to 7. The marks for each question are shown in brackets at the end of each question. 1. Resistances of 5, 7, and 8 are connected in series. If a 10V suppy votage is connected across the arrangement determine the current fowing through and the p.d. across the 7 resistor. Cacuate aso the power dissipated in the 8 resistor. (6) 2. For the series-parae network shown in Fig. R2.1, find (a) the suppy current, (b) the current fowing through each resistor, (c) the p.d. across each resistor, (d) the tota power dissipated in the circuit, (e) the cost of energy if the circuit is connected for 80 hours. Assume eectrica energy costs 14p per unit. (15) 3. The charge on the pates of a capacitor is 8 mc when the potentia between them is 4 kv. Determine the capacitance of the capacitor. (2) 4. Two parae rectanguar pates measuring 80 mm by 120 mm are separated by 4 mm of mica and carry an eectric charge of 0.48 µc. The votage between the pates is 500V. Cacuate (a) the eectric fux density (b) the eectric fied strength, and (c) the capacitance of the capacitor, in picofarads, if the reative permittivity of mica is 5. (7) 5. A 4 µf capacitor is connected in parae with a 6 µf capacitor. This arrangement is then connected in series with a 10 µf capacitor. A suppy p.d. of 250V is connected across the circuit. Find (a) the equivaent capacitance of the circuit, (b) the votage across the 10 µf capacitor, and (c) the charge on each capacitor. (7) 6. A coi of 600 turns is wound uniformy on a ring of non-magnetic materia. The ring has a uniform cross-sectiona area of 200 mm 2 and a mean circumference of 500 mm. If the current in the coi is 4 A, determine (a) the magnetic fied strength, (b) the fux density, and (c) the tota magnetic fux in the ring. (5) 7. A mid stee ring of cross-sectiona area 4 cm 2 has a radia air-gap of 3 mm cut into it. If the mean ength of the mid stee path is 300 mm, cacuate the magnetomotive force to produce a fux of 0.48 mwb. (Use the B H curve on page 74) (8) R Ω R 2 5 Ω R 3 2 Ω R 5 11 Ω R 4 8 Ω 100 V Figure R2.1

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