electrical mcq
TRANSCRIPT
1. For the following differential equation
2d2y
dt2+ 4
dy
dt+ 8y = 8x
the damping ratio is
A. 1
B. 2
C. 0.5
D. 0.7
Solution: Let x be the input and y be the output.
d2y
dt2+ 2
dy
dt+ 4y = 4x
Taking Laplace transfrom
s2Y (s) + 2sY (s) + 4Y (s) = 4X(s)
The transfer function of the system is given by
Y (s)
X(s)=
4
s2 + 2s + 4
Comparing with the standard form
Y (s)
X(s)=
ω2n
s2 + 2ζω2ns + ω2
n
Therefore, ωn = 2.
2ζωn = 2
ζωn = 1
ζ =1
ωn
=1
2= 0.5
2. The time constant for the differential equation in the above problem is
A. 0.5
B. 1.5
C. 0.2
D. 1.0
Solution: Time constant T = 1
ζωn= 1
3. The open-loop transfer function of a system is
H(s)G(s) =10
s(s + 2)(s + 5)
The system is of type
A. N=0
B. N=1
C. N=2
D. N=3
Solution: The type of a system is the number of poles at the origin.
4. Which of the following is used for Nyquist plot?
A. Characteristic equation
B. Open-loop transfer function
C. Closed-loop transfer function
D. None of these
Solution: Used to determine the stability of closed-loop systems on the basis ofopen-loop response to steady-state sinusoidal inputs.
5. The closed-loop transfer function of the open-loop transfer function, G(s) = ks(1 + sT )
of a unity feedback system is
A. ks2T + s + k
B. ks(1 + sT )
C.k(1 + sT )
s
D. None of these
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Solution: Assuming that the system has a negative feedback, the transfer functionis given by
T (s) =G(s)
1 + G(s)H(s)
=
k
s(1 + sT )
1 +k
s(1 + sT )
=k
s(1 + sT ) + k=
k
s2 T + s + k
6. A unity feedback system has an open-loop gain G(s) = 10s(s + 10)
. The system has a
steady state velocity error of
A. 1
B. 2
C. 0
D. None of these
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