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GATE’22 EE: Daily Practices Quiz 03-Sep-2021

GATE 2022 Important Dates: Organizing Institute for GATE 2022 is the Indian Institute of Technology Kharagpur. For GATE 2022 Exam IIT Kharagpur has released the official notification and Important dates regarding the GATE 2022 Exam. Aspirants preparing for GATE 2022 must check the details regarding GATE 2022 Important Dates. Read the complete article below for the information related to GATE 2022 Important dates.

GATE’22 EE: Daily Practices Quiz 03-Sep-2021

Each question carries 2 marks
Negative marking: 2/3 mark

Total Questions: 05
Total marks: 10
Time: 12 min.

Q1. In the circuit given in the figure, the limiting error in the power dissipation I^2 R in the resistor R is __________%

GATE 2022. GATE ELECTRICAL, GATE 2022 REGISTRATION,GATE QUIZ |_40.1

(a) 12.2
(b) 0.2
(c) 10.2
(d) 10.6

Q2. The no-load ratio of a 50 Hz single phase transformer is 6000/250 V. The maximum
flux in the core is 0.06 Wb. What is the number of primary turns?
(a) 450
(b) 900
(c) 350
(d) 210

Q3. Given a unity feedback system with G(s)=K/(s(s+4))
The value of K for damping ratio of 0.5 is
(a) 1
(b) 2
(c) 4
(d) 16

Q4. Assertion(A): The system having characteristics equations 4s^2 + 6s + 1 = 0 gives
rise to underdamped oscillations for a step input.
Reason(R): The undamped natural frequency of oscillation of the system is ω_n = 0.5
rad/s.
(a) Both A and R are True and R is the correct explanation of A.
(b) Both A and R are True but R is not the correct explanation of A.
(c) A is True but R is False.
(d) A is False but R is True.

Q5. When two coupled coils of equal self-inductance are connected in series in one way. The net inductance is 12 mH and when they are connected in the other way the net inductance is 4 mH. The maximum value of inductance when they are connected in parallel in a suitable way is
(a) 2 mH
(b) 4 mH
(c) 3 mH
(d) 6 mH

SOLUTIONS
S1. Ans.(c)
Sol. The limiting error in the power dissipation I^2 R=2△I+△R=2×5+0.2=10.2 %.

S2. Ans.(a)
Sol. E_1=4.44 f N_1 ϕ_m or 6000=4.44×50×N_1×0.06 ∴N_1=450

S3. Ans.(d)
Sol. Characteristic equation is s² + 4s +k = 0
Compared to second ordered standard characteristic equation:
Natural frequency ωn = √k and 2ξωn = 4
Given: ξ = 0.5,
∴ωn = 4 = √k Therefore, k = 16

S4. Ans.(d)
Sol. Characteristics equation given is
⇒ 4s^2 + 6s + 1 = 0
⇒ s^2 + 6/4s + 1/4 = 0
⇒ s^2 + 3/2s + 1/4 = 0
Comparing this equation with the standard characteristic’s equation s^2+2sζω_n+ω_n^2 we get,
(i) ω_n^2 = 1/4
⇒ ω_n = 1/2 = 0.5 rad/sec
(ii) 2ζω_n = 3/2
⇒ ζ = 3/(4ω_n )
⇒ ζ = 3/(4×0.5 )
⇒ ζ = 3/(2 )
So, ζ = 1.5 > 1
Hence, System is not Underdamped.

GATE 2022. GATE ELECTRICAL, GATE 2022 REGISTRATION,GATE QUIZ |_50.1

 

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