EE153 Homework 1
A.
DC Generators
1. A 4 pole d.c. generator has a wave-wound armature with 792 conductors. The flux per pole is 0.0121 Wb. Determine the speed at which it should be run to gener ate 240 V on no-load. 2. A 20-kW compound generator works on full-load with a terminal voltage of 230 V. The armature, series and shunt field resistances are 0.1, 0.05 and 115 Ω respectively. Calculate the generated e.m.f. when the generator is connected short-shunt. 3. A d.c. generator generates an e.m.f. of 520 V. It has 2,000 armature conductors, flux per pole of 0.013 Wb, speed of 1200 r.p.m. and the armature winding has four parallel paths. Find the number of poles. 4. When driven at 1000 r.p.m. with a flux per pole of 0.02 Wb, a d.c. generator has an e.m.f. of 200 V. If the speed is increased to 1100 r.p.m. and at the same time the flux per pole is reduced to 0.019 flux per pole, what then is the induced e.m.f.? 5. Calculate the flux per pole required on full-load for a 50-kW, 400 V, 8 pole, 600 r.p.m. d.c. shunt generator with 256 conductors arranged in a lap-connected winding. The armature winding resistance is 0.1 Ω, the shunt field resistance is 200 Ω and there is a brush contact voltage drop of 1 V at each e ach brush on full-load. B.
DC Motors
1. Calculate the torque in Newton-meter developed by a 440-V d.c. motor having an armature resistance of 0.25 Ω and running at 750 r.p.m. when taking a current of 60 A. 2. A 4-pole, d.c. motor has a wave-wound armature with 65 slots each containing 6 conductors. The flux per pole is 20 mWb and the armature has a resistance of 0.15 Ω. Calculate the motor speed when the machine is operating from a 250-V supply and taking a current of 60 A. 3. A d.c. shunt motor runs at 900 r.p.m. from a 400 V supply when taking an armature current of 25 A. Calculate the speed at which it will run from a 230-V supply when taking an armature current of 15 A. The resistance of the armature circuit is 0.8 Ω. Assume the flux per pole at 230 V to have decreased to 75% of its value at 400 V. 4. A shunt machine connected to 250-V mains has an armature resistance of 0.12 Ω and field resistance of 100 Ω. Find the ratio of the speed of the machine as a generator to the speed as a motor, if line current is 80 A in both cases. 5. A 20-kW d.c. shunt generator delivering rated output at 1000 r.p.m. has a terminal voltage of 500-V. The armature resistance is 0.1 Ω, voltage drop per brush is 1V and field resistance is 500 Ω. Calculate the speed at which the machine will run as a motor taking an input of 20 kW from a 500 V d.c. supply.
C.
AC Generators
1. Find the no-load phase and line voltage of a star-connected, 4-pole alternator having flux per pole of 0.1 Wb sinusoidally distributed: 4 slots per pole per phase, 3 conductors per slot, doublelayer winding with a coil span of 150°. Assume frequency is 50 Hz. 2. A synchronous generator has 9 slots per pole. If each coil spans 8 slots pitches, what is the value of the pitch factor? 3. If a field excitation of 10 A in a certain alternator gives a current of 150 A on short-circuit and a terminal voltage of 900 V on open-circuit, find the internal voltage drop with a load current of 60 A. D.
AC Motors
1. In the case of an 8-pole induction motor, the supply frequency was 50-Hz and the shaft speed was 735 r.p.m. What were the magnitudes of the following: (a) synchronous speed (b) speed of slip (c) per unit slip (d) percentage slip. E.
Transformers
1. The number of turns on the primary and secondary windings of a 1- φ transformer are 350 and 35 respectively. If the primary is connected to a 2.2 kV, 50-Hz supply, determine the secondary voltage on no-load. 2. A 3000/200-V, 50-Hz, 1-phase transformer is built on a core having an effective cross-sectional 2 area of 150 cm and has 80 turns in the low-winding. Calculate: (a) the value of the maximum flux density in the core; (b) the number of turns in the high vo ltage winding.
