NEET Physics Notes - Chapter 23

1 60 Electromagnetic Induction Chapter E3 23 Electromagnetic Induction is produced in the circuit called induced emf. The induced emf ID Magnetic Flux (1) The total number of magnetic lines of force passing persists only as long as there is change or cutting of flux. (2) Second law : The induced emf...

1 60 Electromagnetic Induction Chapter E3 23 Electromagnetic Induction is produced in the circuit called induced emf. The induced emf ID Magnetic Flux (1) The total number of magnetic lines of force passing persists only as long as there is change or cutting of flux. (2) Second law : The induced emf is given by rate of change of normally through an area placed in a magnetic field is equal to the magnetic flux linked with that dA area. U N d ; Negative sign indicates that induced emf (e) dt opposes the change of flux. (3) Other formulae :  = BA cos ; Hence  will change if Fig. 23.1 either, B, A or  will change So e   N   (2) Net flux through the surface   B  d A  BA cos θ   ( is the angle between area vector and magnetic field If  = then  = BA, If  = U vector) 0o 90o then  = 0 (3) Unit and Dimension : Magnetic flux is a scalar quantity. ST It’s S.I. unit is weber (wb), CGS unit is Maxwell or Gauss × cm2; ( 1 wb  10 8 Maxwell ). Table 23.1 : Induced i, q and P Induced current (i) i e N d . R R dt dimensional formula [] = [ML2T–2A–1] Faraday's Laws of Electromagnetic Induction (1) First law : Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit changes an emf Induced charge ( q) dq  i dt   N  d R Induced charge is time independent. N  m Joule Volt Coulomb   Amp Amp Amp  Volt sec = Ohm × Coulomb = Henry × Amp. It’s d N (2  1 ) NA (B2  B1 ) cos    dt t t NBA(cos 2  cos1 ) t (4) Other units : Tesla × m2  d . For N turns dt e D YG  magnetic flux linked with the circuit i.e. e   B Induced power (P) P e2 N 2  d     R R  dt  2 It depends on time and resistance Lenz's Law This law gives the direction of induced emf/induced current. According to this law, the direction of induced emf or current in a circuit is such as to oppose the cause that produces it. This law is based upon law of conservation of energy. 2 Electromagnetic Induction (1) When N-pole of a bar magnet moves towards the coil, induced current as seen by observer O is in anticlockwise direction. (figure) the flux associated with loop increases and an emf is induced in it. Since the circuit of loop is closed, induced current also flows v in it. S (2) Cause of this induced current, is approach of north pole N N Observer and therefore to oppose the cause, i.e., to repel the approaching Fig. 23.2 60 north pole, the induced current in loop is in such a direction so that the front face of loop behaves as north pole. Therefore Position of magnet Direction of induced N S G Observer Magnetic field linked with the coil and it’s progress as viewed from left G S N S Clockwise direction Clockwise direction Anticlockwise direction As a north pole As a south pole As a south pole As a north pole Repulsive force Attractive force Dots () Increases Dots () Decreases U Repulsive force Attractive force Cross (×), Increases Cross (×), Decreases (3) If the loop is free to move the cause of induced emf in U the coil can also be termed as relative motion. Therefore to oppose the cause, the relative motion between the approaching ST magnet and the loop should be opposed. For this, the loop will itself start moving in the direction of motion of the magnet. (4) It is important to remember that whenever cause of induced emf is relative motion, the new motion is always in the direction of motion of the cause. Induced Electric Field A time varying magnetic field dB dt always produced induced electric field in all space surrounding it. Induced electric field (Ein) is directly proportional to induced   emf so e  Ein  d l..…(i)  From Faraday's second laws e   d dt..…(ii)   d From (i) and (ii) e  Ein.d l   dt  This is known as integral form of Faraday’s laws of EMI. It is non-conservative and non-electrostatic in nature. Its field lines are concentric circular closed curves. G Observer Observer D YG force opposed N Anticlockwise direction the coil Type of magnetic G Observer current Behaviour of face of N ID S E3 Table 23.2 : The various positions of relative motion between the magnet and the coil dB/dt in cylindrical space           Concentric circular field lines of induced electric field (A)    B(t)                  a      existing everywhere inside and outside Fig. of 23.3 cylindrical space  (B) r P Electromagnetic Induction A uniform but time varying magnetic field B(t) exists in a 1295 (3) Motion of conducting rod on an inclined plane : When circular region of radius ‘a’ and is directed into the plane of the conductor start sliding from the top of an inclined plane as paper as shown, the magnitude of the induced electric field ( Ein) shown, it moves perpendicular to it’s length but at an angle at point P lies at a distance r from the centre of the circular direction ofBmagnetic field. (90   ) with the Q where r  a or E   a 2 dB 1 ; E in  2r dt r Dynamic (Motional) EMI Due to Translatory Motion directed into the plane of the paper. Let the rod be moving to the right as shown in figure. The conducting electrons also move to × × × × × × P × ++ × e × v × × × × × × × × × – – Q × F × × × × × e  Bv sin(90   )l  Bvl cos So induced current i  Bvl cos  (Directed from Q to P). R The forces acting on the bar are shown in following figure. The rod will move down with constant velocity only if D YG × × Hence induced emf across the ends of conductor U the right as they are trapped within the rod.  (B) Fig. 23.6 ID (1) Consider a conducting rod of length l moving with a   uniform velocity v perpendicular to a uniform magnetic field B , (90 – ) mg cos (90–) mg R (A) R  E3  Fm v P   d dB dB i.e. E(2r)  a 2 Eind l  e  A dt dt dt 60 region is calculated as follows. So Fm cos Fig. 23.4 mgR sin θ  Bv l cos   B T  l cos   mg sin  v T  2 2 R B l cos 2 θ   Motional Emi in Loop by Generated Area If conducting rod moves on two parallel conducting rails as force shown in following figure then phenomenon of induced emf can Fm  evB. So they move from P to Q within the rod. The end P also be understand by the concept of generated area (The area of the rod becomes positively charged while end Q becomes swept of conductor in magnetic field, during it’s motion) U Conducting electrons experiences a magnetic Fm cos  mg cos(90   )  mg sin  Bil cos   mg sin negatively charged, hence an electric field is set up within the ST rod which opposes the further downward movement of electrons i.e. an equilibrium is reached and in equilibrium Fe = Fm i.e. eE = evB or E = vB  Induced emf e  El  Bvl [ E  × of magnetic field or length. Induced emf e = Bvl sin       × × × V ] l (2) If rod is moving by making an angle  with the direction  × ×P × × × l R × × × × × Q v × × × × × × v × × × × × × vt Fig. 23.7 As shown in figure in time t distance travelled by conductor = vt v sin  v cos  v  B (A) l      v (B) Fig. 23.5   l sin   Area generated A = lvt. Flux linked with this area  = BA = d  Bvl Blvt. Hence induced emf | e |  dt 1296 Electromagnetic Induction (1) Induced current : i  Bvlv where l = length of the axle or distance between the tips of Bvl e  R R (2) Magnetic force : Conductor PQ experiences a magnetic force in opposite direction of it’s motion and B 2vl 2  Bvl  Fm  Bil  B l  R  R  the wings of plane, Bv = vertical component of earth's magnetic field and v = speed of train or plane. Motional EMI Due to Rotational Motion (1) Conducting rod : A conducting rod of length l whose one end is fixed, is rotated about the axis passing through it’s fixed motion of rod PQ, the rate of doing mechanical work by external end and perpendicular to it’s length with constant angular agent or mech. Power delivered by external source is given as velocity . Magnetic field (B) is perpendicular to the plane of the paper. (4) Electrical power : Also electrical power dissipated in resistance or rate of heat dissipation across resistance is given as emf induces across the ends of the rod where 2 Pthermal  H  Bvl   i2 R   .R ; t  R  2 2 2 B v l R Pthermal    =   (revolution per sec) and T =   Time period.  Q (5) Motion of conductor rod in a vertical plane : If then with rise in it’s speed (v), induces emf (e), induced current constant. identical cells connected in    D YG  Rod will achieve a constant maximum (terminal) velocity vT 2 2 B l × × × × × × × × × × × × mg × × × × R l t=0 × × × Fm × × × × mg U Fig. 23.8 parallel  ST Motion of train and aeroplane in earth's magnetic field e net  e fashion  O         B l    (emf of single cell). Let N be       the number of spokes hence 1 e net  Bwl 2 ;  2 2       Fig. 23.11 Here e net  N o i.e. total emf does not depends on number of spokes ‘N’. (3) Special cases (A)   Due to flux cutting each metal spoke becomes identical cell  mgR  P shown below in fig.  vT    Fig. 23.10 of emf e (say), all such  l  B   (i), magnetic force (Fm) increases but it’s weight remains B 2 v T2 l 2  mg R  is rotating with angular velocity  in a given magnetic field as U conducting rod released from rest (at t = 0) as shown in figure So  (2) Cycle wheel : A conducting wheel each spoke of length l principle of conservation of energy.) if Fm  mg   frequency   ID (It is clear that Pmech. = Pthermal which is consistent with the  E3 Pmech  Pext B 2v 2 l 2 dW B 2 vl 2   Fext. v  v  dt R R 60 (3) Power dissipated in moving the conductor : For uniform Faraday copper disc  B  generator : A metal disc can be assumed to made of uncountable radial conductors when metal disc O r rotates in transverse magnetic field these radial conductors cuts Fig. 23.9 (B) away magnetic field lines and Fig. 23.12 because of this flux cutting all becomes identical cells each of Induced emf across the axle of the wheels of the train and it is across the tips of the wing of the aeroplane is given by e = emf ‘e’ where e  1 B r 2 , 2 Electromagnetic Induction (4) Semicircular conducting loop : If a semi-circular conducting loop (ACD) of radius  C r loop being in the plane of paper. S  A  r       B  O The loop is now made to rotate with a constant angular velocity , B about an axis passing through O  = t will always be found in an electrical circuit whether we want it or circuit will have lesser value of inductance. (4) Inductance is analogous to inertia in mechanics, Flux link with the rotating loop at time t   BA the loop in magnitude because inductance of an electrical circuit opposes any change of current in the circuit. ID in (3) A straight wire carrying current with no iron part in the E3 dA r 2 1 1  A  r(r )  r 2 t ; dt 2 2 2 | e| d dA Br 2 B r 2 and induced current i  | e| B   dt dt 2R 2 R Self Induction Whenever the electric current passing through a coil or Periodic EMI Suppose a rectangular coil having N turns placed initially in circuit changes, the magnetic flux linked with it will also change. magnetic As a result of this, in accordance with Faraday’s laws of field such U a (2) Inductance is inherent property of electrical circuits. It not. In time t the area swept by the loop in the field i.e. region II emf (1) Inductance is that property of electrical circuits which opposes any change in the current in the circuit. Fig. 23.13 resistance of the loop is R. induced Inductance  and perpendicular to the plane of paper. The effective Hence t, (2) Induced current : At any time e0 e i  sin  t  i0 sin  t where i0 = current amplitude or max. R R e NBA   0  current i0  0   R R R 60 ‘r’ with centre at O, the plane of 1297 that  = 2 magnetic field is perpendicular to D YG it’s plane as shown.  B n̂  – Angular speed  – Frequency of rotation of coil R – Resistance of coil For uniform rotational motion R electromagnetic induction, an emf is induced in the coil or the circuit which opposes the change that causes it. This phenomenon is called ‘self induction’ and the emf induced is called back emf, current so produced in the coil is called induced current. Induced current Induced current Fig. 23.14 U with , the flux linked with coil at any time t   NBA cos  NBA cos t ST   0 cos ωt where 0 = NBA = maximum flux (1) Induced emf in coil : Induced emf also changes in periodic manner that’s why this phenomenon called periodic Rheostat Key (A) Main current increasing Rheostat Key (B) Main current decreasing Fig. 23.15 EMI e d  NBA  sin t  e  e 0 sinωt dt amplitude or max. emf  NBA    0  where e0 = emf (1) Coefficient of self-induction : Number of flux linkages with the coil is proportional to the current i. i.e. N  i or N  Li (N is the number of turns in coil and N – total flux N = coefficient of self-induction. linkage). Hence L  i 1298 Electromagnetic Induction (2) If i = 1amp, N = 1 then, L =  i.e. the coefficient of self induction of a coil is equal to the flux linked with the coil when the current in it is 1 amp. (3) By Faraday’s second law induced emf e   N d. dt Toroid Winding di di Which gives e   L ; If  1 amp / sec then |e|= L. dt dt L Hence coefficient of self induction is equal to the emf 0 N 2r Core 2 60 induced in the coil when the rate of change of current in the coil is unity. (4) Units and dimensional formula of ‘L’ : It's S.I. unit  volt  sec  ohm  sec. But practical unit is henry (H). It’s amp L dimensional formula [L] = [ML2T–2A–2] 2 2 0 N 2 a  ID (5) Dependence of self inductance (L) : ‘L’ does not depend E3 Square coil weber Tesla  m 2 N m Joule Coulomb  volt     Amp Amp Amp 2 Amp 2 Amp 2 upon current flowing or change in current flowing but it depends upon number of turns (N), Area of cross section (A) and ‘L’ does not play any role till there is a constant current O Coaxial cylinders L r1 r 0 r log e 2 2r r1 l U permeability of medium (). r i 2.303 r 0 log10 2 2r r1 r2 D YG flowing in the circuit. ‘L’ comes in to the picture only when there is a change in current. (6) Magnetic potential energy of inductor : In building a steady current in the circuit, the source emf has to do work against of self inductance of coil and whatever energy consumed for this work stored in magnetic field of coil this energy called as magnetic potential energy (U) of coil  U U N i 1 1 Lidi  Li 2 ; Also U  (Li)i  2 2 2 i 0 ST (7) The various formulae for L Condition Whenever the current passing through a coil or circuit changes, the magnetic flux linked with a neighbouring coil or circuit will also change. Hence an emf will be induced in the neighbouring coil or circuit. This phenomenon is called ‘mutual induction’. i1 Figure 0N 2r i2 Variable current Circular coil L Mutual Induction P S M 2 Fig. 23.16 Solenoid L l  0 r N 2 A N 2 A (   0 r )  l l i Load R Electromagnetic Induction 1299 (1) Coefficient of mutual induction : Total flux linked with the secondary due to current in the primary is N2 2 and (A) k=1 (B) 0 < k < 1 (C) k=0 N2 2  i1  N 2  2  Mi 1 where N1 - Number of turns in primary; N2 - Number of turns in secondary; 2 - Flux linked with each turn of secondary; i1 - Current flowing through (7) The various formulae for M : Condition primary; M-Coefficient of mutual induction or mutual inductance. i coils R M  di1 1 Amp then |e2| = M. Hence coefficient of  dt sec mutual induction is equal to the emf induced in the secondary  0 N 1 N 2 r 2 S 2R Two Solenoids coil when rate of change of current in primary coil is unity. (4) Units and dimensional formula of M : Similar to selfinductance (L) (5) Dependence of mutual inductance l i1 μ0 N1 N 2 A l ID M P r E3 di d 2 secondary e 2   N 2 ; e 2  M 1 dt dt 60 Two concentric coplaner circular (2) According to Faraday’s second law emf induces in (3) If Figure Secondar Primary y (N 2 (N1 turns) turns) U Two concentric coplaner square coils (i) Number of turns (N1, N2) of both coils D YG (ii) Coefficient of self inductances (L1, L2) of both the coils M 0 2 2 N1 N 2l L (1) (2) i 2 l L (iii) Area of cross-section of coils (iv) Magnetic permeability of medium between the coils ( r) or nature of material on which two coils are wound (v) Distance between two coils (As d increases so M U decreases) (vi) Orientation between primary and secondary coil (for 90o orientation no flux relation M = 0) ST (6) Relation between M, L1 and L2 : For two magnetically coupling factor which is defined as P Air gap that the mutual induction between them is negligible, then net self inductance LS  L1  L2 inductance LS  L1  L2  2 M having mutual inductance are connected in parallel and are far from each other, then net inductance L is Magnetic flux linked in secondary ; Magnetic flux linked in primary S mutual inductance are in series and are far from each other, so (2) Parallel : If two coils of self-inductances L1 and L2 coupled coils M  k L1 L 2 ; where k – coefficient of coupling or P (1) Series : If two coils of self-inductances L1 and L2 having When they are situated close to each other, then net (vii) Coupling factor ‘K’ between primary and secondary coil k Combination of Inductance S Fig. 23.17 0k1 P S LP  1 1 1    LP L1 L2 L1 L2 L1  L2 When they are situated close to each other, then 1300 Electromagnetic Induction LP  L1 L2  M 2 L1  L2  2 M LC- Oscillation Growth and Decay of Current In LR- Circuit When a charged capacitor C having an initial charge q0 is series with a battery and a key then on closing the circuit current discharged through an inductance L, the charge and current in through the circuit rises exponentially and reaches up to a the circuit start oscillating simple harmonically. If the resistance certain maximum value (steady state). If circuit is opened from of the circuit is zero, no energy is dissipated as heat. We also L it’s steady state condition then current through Lthe circuit Induced decreases exponentially. current away from the circuit. The total energy associated with the current circuit is constant. Main + current + current K B (A) Growth of current Fig. 23.18 assume an idealized situation in which energy is not radiated Frequency of oscillation is given by E3 Main Induced 60 If a circuit containing a pure inductor L and a resistor R in K B (B) Decay of current   1 rad LC sec 1 + Hz ID or   (1) The value of current at any instant of time t after closing 2 LC q0 – C Fig. 23.20 Eddy Current When a changing magnetic flux is applied to a bulk piece of U the circuit (i.e. during the rising of current) is given by L conducting material then circulating currents called eddy R   t E i  i 0 1  e L  ; where i0  imax  = steady state current. R     D YG currents are induced in the material. Because the resistance of (2) The value of current at any instant of time t after opening from the steady state condition (i.e. during the decaying of current) is given by i  i0 e  R t L (3) Time constant () : It is given as   L ; It’s unit is R U second. In other words the time interval, during which the current in an inductive circuit rises to 63% of its maximum value the bulk conductor is usually low, eddy currents often have large magnitudes and heat up the conductor. (1) These are circulating currents like eddies in water. (2) Experimental concept given by Focault hence also named as “Focault current”. (3) The production of eddy currents in a metallic block leads to the loss of electric energy in the form of heat. ST at make, is defined as time constant or it is the time interval, during which the current after opening an inductive circuit falls to i i0 maximum value. 37% of its i t= weakening them and also reducing losses causes by them i = 0.37i0 t (A) for circulation of eddy current increases, resulting in to i0 i = 0.63i0 (4) By Lamination, slotting processes the resistance path t= Fig. 23.19 (B) Plane metal Slotted metal plate plate t × × × × × × × × × × × × × × × × × × (A) Strong eddies (B) Feeble eddies produced Gradual damping Cause excessive electro B magnetic damping Feeble eddy currents Strong eddy currents Electromagnetic Induction 1301 (v) Energy meter : In energy meters, the armature coil carries a metallic aluminium disc which rotates between the poles of a pair of permanent horse shoe magnets. As the armature rotates, the current induced in the disc tends to oppose the motion of the armature coil. Due to this braking dc Motor 60 effect, deflection is proportional to the energy consumed. It is an electrical machine which converts electrical energy eddy currents are undesirable but they find some useful means one whose pointer comes to rest in the final equilibrium without any oscillation about the currents induced in the A R1 N provide electromagnetic damping. (ii) Electric-brakes : When the train is running its wheel is C  F2  F1 frame D YG eddy (2) Construction : It consists of the following components figure. B This is achieved by winding the coil on a metallic frame the large rotates the coil. U equilibrium position when a current is passed in its coil. placed in the magnetic field experiences a torque. This torque ID (i) Dead-beat galvanometer : A dead beat galvanometer immediately (1) Principle : It is based on the fact that a current carrying coil applications as enumerated below position into mechanical energy. E3 (5) Application of eddy currents : Though most of the times S R2 N D S D B2 B1 B C R2 R1 A B2 B1 moving in air and when the train is to be stopped by electric breaks the wheel is made to move in a field created by (A) Fig. 23.22 (B) electromagnet. Eddy currents induced in the wheels due to the U changing flux oppose the cause and stop the train. (iii) Induction furnace : Joule's heat causes the melting of a ST metal piece placed in a rapidly changing magnetic field. (iv) Speedometer : In the speedometer of an automobile, a magnet is geared to the main shaft of the vehicle and it rotates according to the speed of the vehicle. The magnet is mounted in an aluminium cylinder with the help of hair springs. When the magnet rotates, it produces eddy currents in the drum and drags it through an angle, which indicates the speed of the vehicle on a calibrated scale. ABCD = Armature coil, S1, S2 = split ring comutators B1, B2 = Carbon brushes, N, S = Strong magnetic poles (3) Working : Force on any arm of the coil is given by    F  i(l  B) in fig., force on AB will be perpendicular to plane of the paper and pointing inwards. Force on CD will be equal and opposite. So coil rotates in clockwise sense when viewed from top in fig. The current in AB reverses due to commutation keeping the force on AB and CD in such a direction that the coil continues to rotate in the same direction. 1302 Electromagnetic Induction (4) Back emf in motor : Due to the rotation of armature coil lifts, dc drills, fans and blowers, centrifugal pumps and air in magnetic field a back emf is induced in the circuit. Which is compressors, etc. given by e = E – iR. ac Generator/Alternator/Dynamo An electrical machine used to convert mechanical energy Back emf directly depends upon the angular velocity  of armature and magnetic field B. But for constant magnetic field B, value of back emf e is given by e   or e = k into electrical energy is known as ac generator/alternator. (e = (1) Principle : It works on the principle of electromagnetic (5) Current in the motor : i  E  e E  k ; When motor  R R 60 induction i.e., when a coil is rotated in uniform magnetic field, an NBA sint) induced emf is produced in it. (2) Construction : The main components of ac generator are E is just switched on i.e.  = 0 so e = 0 hence i   maximum R C E3 B and at full speed,  is maximum so back emf e is maximum and i is minimum. Thus, maximum current is drawn when the motor is just switched on which decreases when motor attains the N speed. A ID R1 (6) Motor starter : At the time of start a large current flows D B1 RL through the motor which may burn out it. Hence a starter is used R2 U for starting a dc motor safely. Its function is to introduce a suitable resistance in the circuit at the time of starting of the S Output B2 Fig. 23.24 motor. This resistance decreases gradually and reduces to zero R C H 1 D YG when the motor runs at full sped. R R 2 3 R 4 Spring 5 6 E M dc mains (i) Armature : Armature coil (ABCD) consists of large number R ST U Fig. 23.23 of turns of insulated copper wire wound over a soft iron core. (ii) Strong field magnet : A strong permanent magnet or an electromagnet whose poles (N and S) are cylindrical in shape in a field magnet. The armature coil rotates between the pole pieces of the field magnet. The uniform magnetic field provided by the field magnet is perpendicular to the axis of rotation of the coil. The value of starting resistance is maximum at time t = 0 (iii) Slip rings : The two ends of the armature coil are and its value is controlled by spring and electromagnetic system connected to two brass slip rings R1 and R2. These rings rotate and is made to zero when the motor attains its safe speed. (7) Mechanical power and Efficiency of dc motor : P P e Back e.m.f. Efficiency   mechanical  out   Psup plied Pin E Supply voltage (8) Uses of dc motors : They are used in electric locomotives, electric ears, rolling mills, electric cranes, electric along with the armature coil. (iv) Brushes : Two carbon brushes (B1 and B2), are pressed against the slip rings. The brushes are fixed while slip rings rotate along with the armature. These brushes are connected to the load through which the output is obtained. Electromagnetic Induction 1303 (3) Working : When the armature coil ABCD rotates in the It consists of two coils wound on the same core. The magnetic field provided by the strong field magnet, it cuts the alternating current passing through the primary creates a magnetic lines of force. Thus the magnetic flux linked with the continuously changing flux through the core. This changing flux coil changes and hence induced emf is set up in the coil. The induces an alternating emf in the secondary. direction of the induced emf or the current in the coil is Laminated sheets The current flows out through the brush B1 in one direction ~ Input Source Iron core revolution in the reverse direction. This process is repeated. Fig. 23.26 Therefore, emf produced is of alternating nature. Nd   NBA  sint = e0 sint dt where e0 = NBA (1) Transformer works on ac only and never on dc. E3 e Output 60 of half of the revolution and through the brush B2 in the next half Load determined by the Fleming’s right hand rule. e e i   0 sint  i0 sint R Resistance of the circuit R R (2) It can increase or decrease either voltage or current but not both simultaneously. dc Generator (3) Transformer does not change the frequency of input ac. then the generator is called dc generator. dc generator consists of (i) Armature (coil) ID If the current produced by the generator is direct current, (4) There is no electrical connection between the winding (ii) Magnet but they are linked magnetically. (5) Effective resistance between primary and secondary winding is infinite. U (iii) Commutator (iv) Brushes In dc generator commutator is used in place of slip rings. (6) The flux per turn of each coil must be same i.e.  S   P ; The commutator rotates along with the coil so that in every cycle D YG when direction of ‘e’ reverses, the commutator also reverses or makes contact with the other brush so that in the external load the current remains in the some direction giving dc Armature U S (Coil) Commutator Brushes – ST + N Load Fig. 23.25  d S d  P. dt dt (7) If NP = number of turns in primary, NS = number of turns in secondary, VP = applied (input) voltage to primary, VS = Voltage across secondary (load voltage or output), eP = induced emf in primary ; eS = induced emf in secondary,  = flux linked with primary as well as secondary, iP = current in primary; iS = current in secondary (or load current) As in an ideal transformer there is no loss of power i.e. Pout  Pin so VS iS  VPiP It is a device which raises or lowers the voltage in ac VP  e P , VS  e S. Hence ratio) Table 23.3 : Types of transformer Step up transformer Transformer and eS N V i  S  S  P  k ; k = Transformation ratio (or turn eP NP VP iS It increases voltage and decreases current Step down transformer It decreases voltage and increases current circuits through mutual induction. P S P S 1304 Electromagnetic Induction energy is lost due to hysteresis. However, the loss of energy can be minimised by selecting the material of core, which has a narrow hysterisis loop. Therefore core of transformer is made of soft iron. Now a days it is made of “Permalloy” ( Fe-22%, Ni78%). VS < VP NS > NP NS < NP (iv) Magnetic flux leakage : Magnetic flux produced in the ES > EP ES < EP primary winding is not completely linked with secondary iS < iP iS > iP because few magnetic lines of force complete their path in air RS > RP RS < RP tS > tP tS > tP k>1 k VP only. To minimize this loss secondary winding is kept inside the E3 primary winding. (v) Humming losses : Due to the passage of alternating current, the core of the transformer starts vibrating and (8) Efficiency of transformer () : Efficiency is defined as produces humming sound. Thus, some part (may be very small) ID the ratio of output power and input power of the electrical energy is wasted in the form of humming P V i i.e.  %  out  100  S S  100 Pin VP i P sounds produced by the vibrating core of the transformer. (10) Uses of transformer : A transformer is used in almost of practical transformer lies between 70% – 90%) D YG For practical transformer Pin  Pout  Plosses U For an ideal transformer Pout = Pin so   100% (But efficiency P Pout (P  PL )  100  in  100 so   out  100  Pin (Pout  PL ) Pin all ac operations e.g. (i) In voltage regulators for TV, refrigerator, computer, air conditioner etc. (9) Losses in transformer : In transformers some power is (ii) In the induction furnaces. always lost due to, heating effect, flux leakage eddy currents, (iii) Step down transformer is used for welding purposes. hysteresis and humming. (iv) In the transmission of ac over long distance. (i) Cu loss ( i 2 R) : When current flows through the Transmission lines U transformer windings some power is wasted in the form of heat (H  i 2 Rt). To minimize this loss windings are made of thick Cu ST wires (To reduce resistance) (ii) Eddy current loss : Some electrical power is wasted in the form of heat due to eddy currents, induced in core, to G Low High V V Power Step up Station transformer Low House or Load V factory High V Step down transforme Fig. 23.27 r minimize this loss transformers core are laminated and silicon is added to the core material as it increases the resistivity. The material of the core is then called silicon-iron (steel). (iii) Hystersis loss : The alternating current flowing through the coils magnetises and demagnetises the iron core again and again. Therefore, during each cycle of magnetisation, some (v) Step down and step up transformers are used in electrical power distribution. (vi) Audio frequency transformers are used in radiography, television, radio, telephone etc. Electromagnetic Induction (vii) Radio frequency transformers are used in radio communication. 1305 the north-south direction, then no potential difference or emf will be induced. (viii) Transformers are also used in impedance matching.  When a conducting rod moving horizontally on equator of earth no emf induces because there is no vertical component of earth's magnetic field. But at poles BV is maximum so maximum flux cutting hence emf induces.  When a conducting rod falling freely in earth's magnetic then due to the flux changes an emf, current and charge induces in the coil. If speed of magnet increases then induced i1 increases but vinduced i2 2 (> v1) charge remains v1 induced current emf and same S N S N induced emf continuously increases w.r.t. time and induced current flows from West - East.  1 henry = 109 emu of inductance or 109 ab-henry.  Inductance at the ends of a solenoid is half of it's the E3  If a bar magnet moves towards a fixed conducting coil, 60 field such that it's length lies along East - West direction then 1   inductance at the centre.  Lend  Lcentre . 2    A thin long wire made up of material of high resistivity ID behaves predominantly as a resistance. But it has some amount of inductance as well as capacitance in it. It is thus difficult to obtain pure resistor. Similarly it is difficult to obtain Induced parameter : e1, i1, q1 e2 (> e1), i2( > i1), q2 (= q1) pure capacitor as well as pure inductor.  Due to inherent presence of self inductance in all when produced by a changing magnetic field. electrical circuits, a resistive circuit with no capacitive or  No flux cutting  No EMI    Vector form of motional emf : e  (v  B).l    In motional emf B, v and l are three vectors. If any two D YG  U  Can ever electric lines of force be closed curve ? Yes, vector are parallel – No flux cutting.             l        v l   B || l so e = 0 U v l v   v || B so e = 0 ST   v || l so e = 0  B  B  A piece of metal and a piece of non-metal are dropped from the same height near the surface of the earth. The non- inductive element in it, also has some inductance associated with it. The effect of self-inductance can be eliminated as in the coils of a resistance box by doubling back the coil on itself.  It is not possible to have mutual inductance without self inductance but it may or may not be possible self inductance without mutual inductance.  If main current through a coil increases (i) so positive (+ve), hence induced emf e will be negative (i.e. opposite emf)  Enet  E  e E  If an aeroplane is landing down or taking off and its wings are in the east-west direction, then the potential E K metallic piece will reach the ground first because there will be no induced current in it. di will be dt Circuit is made on  e  L or i increasing e i di dt i difference or emf will be induced across the wings. If an aeroplane is landing down or taking off and its wings are in  Sometimes at sudden opening of key, because of high 1306 Electromagnetic Induction inductance of circuit a high momentarily induced emf produced and a sparking occurs at key position. To avoid sparking a capacitor is connected across the key.  Sometimes at sudden opening of key, because of high inductance of circuit a high momentarily induced emf produced and a sparking occurs at key position. To avoid sparking a capacitor is connected across the key. 60  One can have resistance with or without inductance but one can’t have inductance without having resistance. that of a resistor. while a resistor opposes the current i, an di inductor opposes the change in the circuit. i i dt b a b a R Vab  L di dt ID Vab = iR L E3  The circuit behaviour of an inductor is quite different from  In RL-circuit with dc source the time taken by the current U to reach half of the maximum value is called half life time and L it is given by T = 0.693. R  dc motor is a highly versatile energy conversion device. It D YG can meet the demand of loads requiring high starting torque, high accelerating and decelerating torque.  When a source of emf is connected across the two ends of the primary winding alone or across the two ends of secondary winding alone, ohm’s law can be applied. But in the transformer as a whole, ohm’s law should not be applied because primary winding and secondary winding are not U connected electrically.  Even when secondary circuit of the transformer is open it also draws some current called no load primary current for ST supplying no load Cu and iron loses.  Transformer has highest possible efficiency out of all the electrical machines.