21. Calculate the steady-state value for x(t)=7e-9t.

A. 0
B. 8
C. 3
D. 1

Answer: A

The steady-state value is obtained at t=∞.

The value of x(t) at t=∞ is 7e-∞=4(0)=0.

The term e-9t is an exponentially decaying function.

22. The maximum Voltage across the capacitor Vc(t)=Vo(1- e-t) is __________

A. Vo
B. 2Vo
C. 3Vo
D. -Vo

Answer: A

The Vc(t)=Vo(1- e-t) is Vo is the transient equation of the capacitor Voltage.

At the steady-state (t=∞) Vc(t)=Vo(1- e-∞) is Vo.

The maximum voltage across the capacitor is Vo.

23. Calculate the value of the coefficient of coupling for the tightly coupled coils.

A. 0
B. 1
C. 3
D. 2

Answer: B

The coefficient of coupling expresses how the two coils are magnetically coupled. It is mathematically represented as

K=M÷√L1.L2.

For tightly coupled coils, the value of the mutual inductance is √L1.L2.

The value of the coefficient of coupling is 1.

24. The maximum current in the inductor IL(t)=Io(1 – e-t/α) is __________

A. Io e-t/α
B. Io
C. 2Io
D. -Io

Answer: B

The IL(t)=Io(1 – e-t/α) is Io is the transient equation of the inductor current.

At the steady-state (t=∞) IL(t)=Io(1- e-∞) is Io.

The maximum current in the inductor is Io.

25. 20 V, 10 A, 10 rpm separately excited dc motor with armature resistance (Ra) equal to .8 ohms. Calculate back emf developed in the motor when it operates on the full load. (Assume rotational losses are neglecteD.

A. 12 V
B. 14 V
C. 13 V
D. 11 V

Answer: A

Back emf developed in the motor can be calculated using the relation

Eb = Vt – I×Ra.

In question, it is asking for a full load. 20 V is terminal Voltage it is fixed so

Eb = 20-10×.8 = 12 V.

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26. Speed of DC shunt motor is directly proportional to___________

A. Eb
B. Φ
C. Vt
D. Ia.Ra

Answer: A

The back e.m.f in case of DC shunt motor is Eb=Vt-Ia.Ra.

The speed in the DC shunt motor is

Eb÷Kv.

The speed is directly proportional to Eb.

27. Calculate the value of the angular acceleration of the DC shunt motor using the given data: J = 1 kg-m2, load torque = 1 N-m, motor torque = 2 N-m.

A. 1 rad/s2
B. 2 rad/s2
C. 3 rad/s2
D. 5 rad/s2

Answer: A

Using the dynamic equation of motor J×(angular acceleration)

= Motor torque – Load torque: 1×(angular acceleration)

= 2-1=1, angular acceleration=1 rad/s^{2}.

28. Calculate the quality factor for the R-L circuit if R=16 Ω and XL=8 Ω with a supply frequency is 1 rad/sec.

A. 2
B. 6
C. 0
D. 7

Answer: A

The quality factor is defined as the ratio of the reactive power to the active power consumed. The resistor always absorbs active power and the inductor absorbs the reactive power.

ΩL=8, L=8 Henry

quality factor=R÷L

=16÷8=2.

29. Calculate the equivalent resistance when two armature resistances are connected in parallel of values 6 Ω, 3 Ω.

A. 3 Ω
B. 2 Ω
C. 4 Ω
D. 7 Ω

Answer: B

When two resistances are connected in parallel their equivalent resistance is equal to the harmonic mean of the individual resistances.

Req=R1.R2÷(R1+R2)

=6×3÷(6+3)=2 Ω.

30. Calculate the quality factor for the R-C circuit if R=1 Ω and C=1 F.

A. 2
B. 4
C. 1
D. 5

Answer: C

The quality factor is defined as the ratio of the reactive power to the active power consumed. The resistor always absorbs active power and the capacitor absorbs the reactive power.