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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 __________%

(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.