CHAPTER 39 ELECTROMAGNETIC INDUCTION

Transcription

1 CHAPTER 39 ELECTROMAGETC DUCTO EXERCSE 8, Page 4. A conductor of length 5 cm is moved at 750 mm/s at right-angles to a uniform flux density of. T. Determine the e.m.f. induced in the conductor. Length, = 5 cm = 0.5 m and velocity, v = 750 mm/s = 0.75 m/s nduced e.m.f., E = B l v sin = sin 90º = Find the speed that a conductor of length 0 mm must be moved at right angles to a magnetic field of flux density 0.6 T to induce in it an e.m.f. of.8. nduced e.m.f., E = B v from which, speed, v = E.8 B = 5 m/s 3. A 5 cm long conductor moves at a uniform speed of 8 m/s through a uniform magnetic field of flux density. T. Determine the current flowing in the conductor when (a) its ends are open- circuited, (b) its ends are connected to a load of 5 ohms resistance. nduced e.m.f., E = B v = =.4 (a) f the conductor is open circuited, then no current will flow. (b) Current, = E.4 = 0.6 A R 5 4. A straight conductor 500 mm long is moved with constant velocity at right angles both to its length and to a uniform magnetic field. Given that the e.m.f. induced in the conductor is.5 and the velocity is 5 m/s, calculate the flux density of the magnetic field. f the conductor forms part of a closed circuit of total resistance 5 ohms, calculate the force on the conductor. 4

2 nduced e.m.f., E = B v i.e..5 = B sin 90º from which, flux density, B = sin 90 = T Force on conductor, F = B sin = E.5 B sin= () (0.500)(sin 00) R 5 = A car is travelling at 80 km/h. Assuming the back axle of the car is.76 m in length and the vertical component of the earth s magnetic field is 40 T, find the e.m.f. generated in the axle due to motion. Generated e.m.f, E = B v = =.56 m 6. A conductor moves with a velocity of 0 m/s at an angle of (a) 90 (b) 45 (c) 30, to a magnetic field produced between two square-faced poles of side length.5 cm. f the flux on the pole face is 60 mwb, find the magnitude of the induced e.m.f. in each case. nduced e.m.f., E = B v sin (a) When = 90, E = B v sin 90 = lvsin sin 90= 48 4 A.5 0 (b) When = 45, E = B v sin 45 = 48 sin 45 = 33.9 (c) When = 30, E = B v sin 30 = 48 sin 30 = 4 7. A conductor 400 mm long is moved at 70 to a 0.85 T magnetic field. f it has a velocity of 5 km/h, calculate (a) the induced voltage, and (b) force acting on the conductor if connected to a 8 resistor. 43

3 5000 (a) nduced voltage, E = B v sin = (0.85)(0.4) (sin 70) = 0.06 or (b) Force on conductor, F = B sin = E B sin= (0.85) 0.06 (0.4)(sin 70) R 8 =

4 EXERCSE 83, Page 44. The mutual inductance between two coils is 50 mh. Find the magnitude of the e.m.f. induced in one coil when the current in the other is increasing at a rate of 30 A/s. The magnitude of the e.m.f. induced, d 30 dt = E M Determine the mutual inductance between two coils when a current changing at 50 A/s in one coil induces an e.m.f. of 80 m in the other. E d M dt hence, mutual inductance, M = 3 E 800 =.6 mh d 50 dt 3. Two coils have a mutual inductance of 0.75 H. Calculate the magnitude of the e.m.f. induced in one coil when a current of.5 A in the other coil is reversed in 5 ms. nduced e.m.f., E M 0.75 d.5.5 dt 5 0 = The mutual inductance between two coils is 40 mh. f the current in one coil changes from 5 A to 6 A in ms, calculate (a) the average e.m.f. induced in the other, (b) the change of flux linked with the other if it is wound with 400 turns. d 5 6 dt 0 = (a) nduced e.m.f., E M (b) E = d Edt from which, change of flux, d = 5.4 mwb dt

5 EXERCSE 84, Page 46. A transformer has 600 primary turns connected to a.5 k supply. Determine the number of secondary turns for a 40 output voltage, assuming no losses. from which, secondary turns, = 96 turns. An ideal transformer with a turns ratio :9 is fed from a 0 supply. Determine its output voltage. and 0 9 from which, output voltage, 0 9 = An ideal transformer has a turns ratio of : and is supplied at 9. Calculate the secondary voltage. from which, secondary voltage, 9 = 6 4. A transformer primary winding connected across a 45 supply has 750 turns. Determine how many turns must be wound on the secondary side if an output of.66 k is required. from which, secondary turns, = 3000 turns 45 46

6 5. An ideal transformer has a turns ratio of 5: and is supplied at 80 when the primary current is 4 A. Calculate the secondary voltage and current., 0 and 4A from which, output voltage, 80 5 from which, secondary current, 4 5 = = 60 A 6. A step-down transformer having a turns ratio of 0: has a primary voltage of 4 k and a load of 0 kw. eglecting losses, calculate the value of the secondary current. 0 and 4000 from which, output voltage, 4000 Secondary power = = 0000 i.e. 00 = = from which, secondary current, = 50 A A transformer has a primary to secondary turns ratio of :5. Calculate the primary voltage necessary to supply a 40 load. f the load current is 3 A determine the primary current. eglect any losses. from which, primary voltage, 40 5 = 6 from which, primary current, 3 5 = 45 A 47

7 8. A 0 resistance is connected across the secondary winding of a single-phase power transformer whose secondary voltage is 50. Calculate the primary voltage and the turns ratio if the supply current is 5 A, neglecting losses. 50 Secondary current, = 7.5 A, 5A and = 50 R 0 from which, primary voltage, = Turns ratio, =.5 or 5 3 or 3: EXERCSE 85, Page 46 Answers found from within the text of the chapter, pages 408 to 46. EXERCSE 86, Page 47. (c). (b) 3. (c) 4. (a) 5. (d) 6. (a) 7. (b) 8. (c) 9. (d) 0. (a). (b). (a) 3. (d) 4. (b) and (c) 48