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GATE’22 EE: Daily Practices Quiz 14-July-2021

Q1-Q2 Carry 1 mark each
Negative marking: 0.33 mark

Q3-Q5 carry 2 marks each
Negative marking: 0.66 mark

Total Questions: 05
Total marks: 8
Time: 12 min.

Q1. In a communication circuit employed to turn-off an SCR, satisfactory turn-off is obtained when
(a) Circuit time constant > device turn-off time
(b) Circuit time constant < device turn-off time
(c) Circuit turn-off time > device turn-off time
(d) Circuit turn-off time < device turn-off time

Q2. If the pu impedance of a single-phase transformer is 0.01+j0.05, then its regulation at 0.8 lagging will be:
(a) 3.8 %
(b) -3.8 %
(c) 2.2 %
(d) -2.2 %

Q3. For a tachometer, if θ (t) is the rotor displace in radians, e(t) is the output voltage and K_t is the tachometer constant in V/rad/sec, then the transfer function E(s)/Ө(s) will be
(a) K_t s^2
(b) K_t \/s
(c) K_t s
(d) K_t

Q4. For the equation, s³ – 4s² + s+6 = 0 the number of roots in the left half of s – plane will be
(a) Zero
(b) One
(c) Two
(d) Three

Q5. Match the items in List-I (to) with the items in List-II (use) and select the correct answer using the codes given below the lists.
List-I List-II
Improve power factor Shunt reactor
Reduces the current ripples Shunt capacitor
Increase the power flow in line Series capacitor
Reduce the Ferranti effect Series reactor
Codes:
A B C D
(a) 2 3 4 1
(b) 2 4 3 1
(c) 4 3 1 2
(d) 4 1 3 2

SOLUTIONS
S1. Ans.(c)
Sol. The circuit should not turn-off before making off the thyristor. i.e., Circuit turn-off time > device turn-off time.

S2. Ans.(a)
Sol. At lagging pf: V.R=(R_pu cos⁡〖ϕ+X_pu sin⁡〖ϕ)×100〗 〗
∴ V.R=(0.01×0.8+0.05×0.6)×100=3.8 %

S3. Ans.(c)
Sol. In A.C. Tachometer output voltage is directly proportional to differentiation of rotor displacement.
e(t)α d/dt [θ(t)]
e(t)=K_i dθ(t)/dt
Taking Laplace transformation on both sides of above equation
E(s)=K_t sθ(s)
So, transfer function
T.F.=E(s)/θ(s) =(K_t )_s

S4. Ans.(b)
Sol.
Given a characteristic equation,
s^3-4s^2+s+6=0
Applying Routh’s method,

 

1 1
-4 6
  0
  6  

There are two sign changes in the first column, so no. of right half poles is 2.
No. of roots in left half of S-plane = (3-2) = 1

S5. Ans.(b)
Sol.
• Shunt reactors are connected at receiving end to improve voltage profile.
• Shunt capacitors are connected at the load end to improve pf of the system.
• Series reactors are connected in series with line and reduces current ripples.
• Series capacitor increases power flow in the line by reducing the net transfer reactance.

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