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GATE’22 EE: Daily Practices Quiz 16-Aug-2021

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

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

Q1. The electric field strength at distant point, P, due to a point charge, +q, located at the origin, is 100 µ V/m. If the point charge is now enclosed by a perfectly conducting metal sheet sphere whose centre is at the origin, then the electric field strength at the point, P, outside the sphere, becomes
(a) Zero
(b) 100 µV/m
(c) – 100 µV/m
(d) 50 µV/m

Q2. The gain margin (in dB) of a system having the loop transfer function
𝐺(𝑠) 𝐻(𝑠) =√2/(s(s+1))
(a) 0
(b)3
(c) 6
(d)∞

Q3. A linear discrete-time system has the characteristics equation,
Z^3-0.81Z=0. The system
(a) is stable
(b)is marginally stable
(c) is unstable
(d)stability cannot be assessed from the given information

Q4. If the open circuit and short circuit impedances of a transmission line are 100 Ω each, what is the characteristic impedance of the line?
(a) 100√2 Ω
(b) 100/√2 Ω
(c) 100 Ω
(d) 200 Ω

Q5. A 100 kVA,1100/220 V, 50Hz single phase transformer gave the following results on open circuit test conducted on LV side. 220 V, 100 A, 6.6 kW. What is the core loss component of current?
(a) 60 A
(b) 50 A
(c) 100 A
(d) 30 A

SOLUTIONS

S1. Ans.(a)
Sol. The point charge +q will induce a charge – q on the surface of metal sheet sphere. Using Gauss’s law, the net electric flux passing through a closed surface is equal to the charge enclosed = + q – q = 0
∴D = 0, E = 0 at point P.

S2. Ans.(d)
Sol. The loop transfer function 𝐺(𝑠) 𝐻(𝑠) =√2/(s(s+1))
It is a second order function, so its gain margin is infinity.

S3. Ans.(a)
Sol. Characteristic equation is given: Z^3-0.81Z=0
∴Z(Z^2-0.81)=0
⇒Z(Z+0.9)(Z-0.9)=0
So, poles are: Z = 0, 0.9 𝑎𝑛𝑑 − 0.9
Note that all three poles are inside the unit circle, so the system is stable.

S4. Ans.(c)
Sol. Z=√(Z_oc×Z_sc )=√(100×100)=100 Ω.

S5. Ans.(d)
Sol. The core loss component of current=I cos⁡ϕ
ACQ: P=6.6 KW=6600 W
∴P=VI cos⁡〖ϕ=6600〗
⇒ I cos⁡ϕ=P/V=6600/220=30 A.

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