1. Calculate the frequency of the waveform x(t)=45sin(40πt+5π).
a) 24 Hz
b) 27 Hz
c) 23 Hz
d) 20 Hz
Explanation: The fundamental time period of the sine wave is 2π. The frequency of x(t) is 40π÷2π=20 Hz. The frequency is independent of phase shifting and time shifting.
2. The generated e.m.f from 16-pole armature having 57 turns driven at 78 rev/sec having flux per pole as 5 mWb, with lap winding is ___________
a) 44.16 V
b) 44.15 V
c) 44.46 V
d) 44.49 V
Explanation: The generated e.m.f can be calculated using the formula Eb = Φ×Z×N×P÷60×A, Φ represent flux per pole, Z represents the total number of conductors, P represents the number of poles, A represents the number of parallel paths, N represents speed in rpm. One turn is equal to two conductors. In lap winding, the number of parallel paths is equal to a number of poles. Eb = .005×16×57×2×4680÷60×16=44.46 V.
3. Calculate the phase angle of the sinusoidal waveform x(t)=42sin(4700πt+2π÷3).
a) 2π÷9
b) 2π÷5
c) 2π÷7
d) 2π÷3
Explanation: Sinusoidal waveform is generally expressed in the form of V=Vmsin(ωt+α) where Vm represents peak value, ω represents angular frequency, α represents a phase difference.
4. Calculate the moment of inertia of the rod about its end having a mass of 39 kg and length of 88 cm.
a) 9.91 kgm2
b) 9.92 kgm2
c) 9.96 kgm2
d) 9.97 kgm2
Explanation:The moment of inertia of the rod about its end can be calculated using the formula I=ML2÷3. The mass of the rod about its end and length is given. I=(39)×.33×(.88)2=9.96 kgm2. It depends upon the orientation of the rotational axis
5. Calculate the moment of inertia of the rod about its center having a mass of 11 kg and length of 29 cm.
a) .091 kgm2
b) .072 kgm2
c) .076 kgm2
d) .077 kgm2
Explanation:The moment of inertia of the rod about its center can be calculated using the formula I=ML2÷12. The mass of the rod about its center and length is given. I=(11)×.0833×(.29)2=.077 kgm2. It depends upon the orientation of the rotational axis.
6. Calculate the shaft power developed by a motor using the given data: Eb = 404V and I = 25 A. Assume frictional losses are 444 W and windage losses are 777 W.
a) 8879 W
b) 2177 W
c) 8911 W
d) 8897 W
Explanation: Shaft power developed by the motor can be calculated using the formula P = Eb*I-(rotational losses) = 404*25- (444+777) = 8879 W. If rotational losses are neglected, the power developed becomes equal to the shaft power of the motor.
7. I Calculate the value of the frequency if the capacitive reactance is 13 Ω and the value of the capacitor is 71 F.
a) .0001725 Hz
b) .0001825 Hz
c) .0001975 Hz
d) .0001679 Hz
Explanation: The frequency is defined as the number of oscillations per second. The frequency can be calculated using the relation Xc=1÷2×3.14×f×C. F=1÷Xc×2×3.14×C = 1÷13×2×3.14×71 = .0001725 Hz.
8. The slope of the V-I curve is 27°. Calculate the value of resistance. Assume the relationship between voltage and current is a straight line.
a) .384 Ω
b) .509 Ω
c) .354 Ω
d) .343 Ω
Explanation: The slope of the V-I curve is resistance. The slope given is 27° so R=tan(27°)=.509 ω. The slope of the I-V curve is reciprocal of resistance.
9. Calculate the active power in a 7481 H inductor.
a) 1562 W
b) 4651 W
c) 0 W
d) 4654 W
Explanation: The inductor is a linear element. It only absorbs reactive power and stores it in the form of oscillating energy. The voltage and current are 90° in phase in case of the inductor so the angle between V & I is 90°. P=VIcos90 = 0 W. Voltage leads the current in case of the inductor.
10. Calculate the active power in a 457 F capacitor.
a) 715 W
b) 565 W
c) 545 W
d) 0 W
Explanation: The capacitor is a linear element. It only absorbs reactive power and stores it in the form of oscillating energy. The voltage and current are 90° in phase in case of the capacitor so the angle between V & I is 90°. P = VIcos90 = 0 W. Current leads the voltage in case of the capacitor.