1. Calculate the value of the frequency of the 220 V DC supply.
a) 10 Hz
b) 0 Hz
c) 20 Hz
d) 90 Hz
Explanation: The frequency is defined as the number of oscillations per second. It is reciprocal of the time period. DC supply magnitude is constant. It does not change with time so the frequency of DC supply is 0 Hz.
2. Calculate the value of the duty cycle if the system is on for 48 sec and off for 1 sec.
a) .979
b) .444
c) .145
d) .578
Explanation: Duty cycle is Ton÷Ttotal. It is the ratio of time for which the system is active and the time taken by the signal to complete one cycle. D = Ton÷Ttotal = 48÷49 = .979
3. Calculate the value of the frequency if the signal completes half of the cycle in 30 sec. Assume signal is periodic.
a) 0.028 Hz
b) 0.016 Hz
c) 0.054 Hz
d) 0.045 Hz
Explanation: The frequency is defined as the number of oscillations per second. It is reciprocal of the time period. It is expressed in Hz. The given signal completes half of the cycle in 30 seconds then it will complete a full cycle in 60 seconds. F = 1÷T = 1÷60 = .016 Hz.
4. Calculate the velocity of the disc if the angular speed is 5 rad/s and radius is 2 m.
a) 25 m/s
b) 20 m/s
c) 25 m/s
d) 10 m/s
Explanation: The velocity of the disc can be calculated using the relation V=ω×r. The velocity is the vector product of angular speed and radius. V = ω×r = 5×2 = 10 m/s.
5. 440 V, 77 A, 700 rpm DC separately excited motor having a resistance of 0.11 ohms excited by an external dc voltage source of 24 V. Calculate the torque developed by the motor on full load.
a) 453.51 N-m
b) 451.24 N-m
c) 440.45 N-m
d) 452.64 N-m
Explanation: Back emf developed in the motor during the full load can be calculated using equation Eb = Vt-I×Ra = 431.53 V and machine constant Km = Eb÷Wm which is equal to 5.88. Torque can be calculated by using the relation T = Km × I = 5.88×77 = 453.51 N-m
6. Calculate the power developed by a motor using the given data: Eb = 55 V and I = 6 A.
a) 440 W
b) 220 W
c) 330 W
d) 550 W
Explanation: Power developed by the motor can be calculated using the formula P = Eb×I = 55×6 = 330 W. If rotational losses are neglected, the power developed becomes equal to the shaft power of the motor
7. Calculate the value of the angular acceleration of the motor using the given data: J = 36 kg-m2, load torque = 66 N-m, motor torque = 26 N-m.
a) 1.11 rad/s2
b) 2.22 rad/s2
c) 3.33 rad/s2
d) 4.44 rad/s2
Explanation: Using the dynamic equation of motor J×(angular acceleration) = Motor torque – Load torque: 36×(angular acceleration) = 66-26 = 40, angular acceleration = 1.11 rad/s2.
8. Calculate the moment of inertia of the apple having a mass of .4 kg and diameter of 12 cm.
a) .0008 kgm2
b) .0007 kgm2
c) .0009 kgm2
d) .0001 kgm2
Explanation: The moment of inertia of the apple can be calculated using the formula I=mr2×.5. The mass of the apple and diameter is given. I=(.4)×.5×(.06)2 = .0007 kgm2. It depends upon the orientation of the rotational axis
9. Calculate the moment of inertia of the thin spherical shell having a mass of 3.3 kg and diameter of .6 cm.
a) .00125 kgm2
b) .00196 kgm2
c) .00145 kgm2
d) .00178 kgm2
Explanation: The moment of inertia of the thin spherical shell can be calculated using the formula I=mr2×.66. The mass of the thin spherical shell and diameter is given. I=(3.3)×.66×(.03)2=.00196 kgm2. It depends upon the orientation of the rotational axis.
10. Calculate the time period of the waveform y(t)=7cos(54πt+2π÷4).
a) .055 sec
b) .037 sec
c) .023 sec
d) .017 sec
Explanation: The fundamental time period of the cosine wave is 2π. The time period of y(t) is 2π÷54π=.037 sec. The time period is independent of phase shifting and time shifting