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speeds. For this part, assume a constant rotational loss of 300 W over the speed range. 4.25 A permanent magnet de motor drives a mechanical load requiring a constant torque of 25 N · m. The motor produces 10 N · m with an armature current of 10 A. The resistance of the armature circuit is 0.2 D. A 200 V de supply is applied to the armature terminals. Determine the speed of the motor. 4.26 A de shunt motor drives an elevator load which requires a constant torque of 300 N · m. The motor is connected to a 600 V de supply and the motor rotates at 1500 rpm. The armature resistance is 0.5 D. (a) Determine the armature current. (b) If the shunt field flux is reduced by 10%, determine the armature current and the speed of the motor. 4.27 A de shunt motor (50 hp, 250 V) is connected to a 230 V supply and delivers power to a load drawing an armature current of 200 amperes and running at a speed of 1200 rpm. Ra = 0.2 D. (a) Determine the value of the generated voltage at this load condition. (b) Determine the value of the load torque. The rotational losses are 500 watts. (c) Determine the efficiency of the motor if the field circuit resistance is 11s n. 4.28 A de shunt machine (23 kW, 230 V, 1500 rpm) has Ra = 0.1 D. 1. The de machine is connected to a 230 V supply. It runs at 1500 rpm at no-load and 1480 rpm at full-load armature current. (a) Determine the generated voltage at full load. (b) Determine the percentage reduction of flux in the machine due to armature reaction at full-load condition. 2. The de machine now operates as a separately excited generator and the field current is kept the same as in part 1. It delivers full load at rated voltage. (a) Determine the generated voltage at full load. (b) Determine the speed at which the machine is driven. (c) Determine the terminal voltage if the load is thrown off. 4.29 A de shunt machine (10 kW, 250 V, 1200 rpm) has Ra = 0.25 D. The machine is connected to a 250 V de supply, draws rated armature current, and rotates at 1200 rpm. (a) Determine the generated voltage, the electromagnetic power developed, and the torque developed. (b) The mechanical load on the motor shaft is thrown off, and the motor draws 4 A armature current. (i) Determine the rotational loss. Problems 205 (ii) Determine speed, assuming no armature reaction. (iii) Determine speed, assuming 10% change in flux due to armature reaction, for a change of armature current from rated value to 4 A. 4.30 A 240 V, 2 hp, 1200 rpm de shunt motor drives a load whose torque varies directly as the speed. The armature resistance of the motor is 0.75 !1. With Ir = 1 A, the motor draws a line current of 7 A and rotates at 1200 rpm. Assume magnetic linearity and neglect armature reaction effect. (a) The field current is now reduced to 0.7 A. Determine the operating speed of the motor. (h) Determine the line current, mechanical power developed, and efficiency for the operating condition of part (a). Neglect rotational losses. 4.31 Repeat Problem 4.30 if the load torque is constant. Determine the torque. 4.32 A 125 V, 5 kW, 1800 rpm de shunt motor requires only 5 volts to send full- load current through the armature when the armature is held stationary. (a) Determine the armature current if full-line voltage is impressed across the armature at starting. (h) Determine the value of the external resistance needed in series with the armature to limit the starting current to 1.5 times the full-load current. (c) The motor is coupled to a mechanical load by a belt. Determine the generated voltage at full-load condition (V, = 125 V, n = 1800 rpm, I a = /a(mtcdl). If the belt breaks, determine the speed of the motor. Neglect rotational losses and assume 10% reduction of flux due to armature reaction at full load. 4.33 A de motor is mechanically connected to a constant-torque load. When the armature is connected to a 120 V de supply, it draws an armature current of value 8 A and runs at 1800 rpm. The armature resistance is Ra = 0.08 !1. Accidentally, the field circuit breaks and the flux drops to the residual flux, which is only 5% of the original flux. (a) Determine the value of the armature current immediately after the field circuit breaks (i.e., before the speed has had time to change from 1800 rpm). (h) Determine the theoretical final speed of the motor after the field cir- cuit breaks. 4.34 At standstill, a de series motor draws 5 amperes and develops 5 N · m torque when connected to a 5 V de supply. The series motor is mechanically coupled to a load. It draws 10 amperes when connected to a 120 V de supply and drives the load at 300 rpm. Assume magnetic linearity. (a) Determine the torque developed by the motor. (h) Determine the value of the external resistance required to be connected in series with the motor. 4.35 A de series motor (230 V, 12 hp, 1200 rpm) is connected to a 230 V supply, draws a current of 40 amperes, and rotates at 1200 rpm. Ra = 0.25 !1 and Rs, = 0.1 n. Assume magnetic linearity. (a) Determine the power and torque developed by the motor. (h) Determine the speed, torque, and power if the motor draws 20 amperes. i .... , ,,. 206 chapter 4 DC Machines 4.36 A 50 hp, 200 V, 1800 rpm shunt motor requires a starter box. During the start, the armature current is constrained within the range 200 to 400 A. The armature circuit resistance is 0.15 !1. Determine the required number of resistors and the value of each resistor in the starter box. 4.37 The Ward-Leonard speed control system shown in Fig. 4.58a uses two identi- cal de machines of rating 250 V, 5 kW, 1200 rpm. The armature resistance of each machine is 0.5 ohms. The generator is driven at a constant speed of 1200 rpm. The magnetization characteristic of each machine at 1200 rpm is as follows: (A) 0.0 I 0.1 I 0.21 0.31 0.41 0.51 0.61 0.71 0.811.0 11.211.4 Ea (V) 5 60 120 160 190 212 230 242 250 262 270 273 Neglect the effect of armature reaction. (a) If the motor field current 11m is kept constant at 0.8 A, determine the maximum and minimum values of the generator field current, l 1g, re- quired for the motor to operate in a speed range of 200 to 1200 rpm at full-load armature current. (b) The generator field current is kept at 1.0 amps and the motor field current is reduced to 0.2 amp. Determine the speed of the motor at full-load armature current. 4.38 Repeat Example 4.11 if a single-phase semiconverter (Fig. 4.60 or Fig. 10.24a) is used to control the speed of the de motor. 4.39 Repeat Example 4.12 if a three-phase semiconverter is used to control the speed of the de motor. 4.40 A de series motor drives an elevator load that requires a constant torque of 200 N · m. The de supply voltage is 400 V and the combined resistance of the armature and series field winding is 0.75 !1. Neglect rotational losses and armature reaction effect. (a) The speed of the elevator is controlled by a solid-state chopper. At 50% duty cycle (i.e., a = 0.5) of the chopper, the motor current is 40 amps. Determine the speed and the horsepower output of the motor and the efficiency of the system. (b) The elevator is controlled by inserting resistance in series with the arma- ture of the series motor. For the speed of part (a), determine the values of the series resistance, horsepower output of the motor, and efficiency of the system. chapter five INDUCTION {ASYNCHRONOUS) MACHINES The induction machine is the most rugged and the most widely used machine in industry. Like the de machine discussed in the preceding chapter, the induction machine has a stator and a rotor mounted on bearings and sepa- rated from the stator by an air gap. However, in the induction machine both stator winding and rotor winding carry alternating currents. The alternating current (ac) is supplied to the stator winding directly and to the rotor winding by induction-hence the name induction machine. The induction machine