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DFCCIL’21 EE: Daily Practices Quiz 28-Aug-2021

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               DFCCIL’21 EE: Daily Practices Quiz 28-Aug-2021

Each question carries 1 mark.
Negative marking: 1/4 mark
Total Questions: 06

Time : 8 min

Q1. A series RLC circuit has a resonant frequency of 1 kHz and a quality factor Q = 100. If each of the R, L and C is doubled from its original value, the new Q of the circuit is:
(a) 25
(b) 50
(c) 100
(d) 200

DFCCIL 2021, DFCCIL ELECTRICAL QUIZ, |_30.1

Q3. By slip test on a 3-phase synchronous generator the maximum and minimum impressed voltages per phase are found to be V_maxand V_min respectively whereas the maximum and minimum phase currents are found to be I_max and I_min respectively. The values of the direct axis synchronous reactance X_d and quadrature axis synchronous reactance X_q are given as
(a) X_d = V_max /I_min ; X_q = V_min/I_max
(b) X_d = V_max/I_min ; X_q = V_min/I_min
(c) X_d = V_max/I_min ; X_q = V_max/I_max
(d) X_d = V_min/I_max ; X_q = V_max/I_min

Q4. For enhancing the power transmission in a long EHV transmission line, the most preferred method is to connect a
(a) Series inductive compensator in the line
(b) Shunt inductive compensator at the receiving end
(c) Series capacitive compensator in the line
(d) Shunt capacitive compensator at the sending end

Q5. Copper shading is provided in energy meter to
(a) Bring flux exactly in quadrature with applied voltage
(b) To increase speed of aluminum disc
(c) To count the rotation
(d) To balance the system from vibration

Q6. The response c(t) of a system is described by the differential equation
(d^2 c(t))/(dt^2 ) + 4(dc(t))/dt + 5c(t) = 0
The system response is
(a) undamped
(b) underdamped
(c) critically damped
(d) oscillatory

SOLUTIONS

S1. Ans.(b)
Sol. Given:
Q = 100
R, L and C are doubled.
Resonant frequency is
ω_o = 2πf_o = √(1/LC)
Quality factor = 1/(ω_o RC)
When R, L, C all are doubled, then
⇒ ω_o^’ = √(1/((2L).(2C)))
⇒ ω_o^’ = 1/2 √(1/LC)
So, ω_o^’ = ω_o/2
Now,
⇒ Q^’ = 1/(ω_o^’ RC)
⇒ Q^’ = 1/(ω_o/2 ×(2R).(2C))
⇒ Q^’ = 1/(2ω_o RC)
⇒ Q^’ = Q/2
⇒ Q^’ = 100/2
So, Q^’ = 50
METHOD 2: USING THE FORMULA FOR QUALITY FACTOR OF SERIES RLC CIRCUIT
I.E., Q=1/R √(L/C)

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S3. Ans.(a)
Sol. X_d = V_max /I_min ; X_q = V_min/I_max

S4. Ans.(c)
Sol. Power flow in line ⍺1/(reactance of the line)
Series capacitive compensation reduces reactance of the line.

S5. Ans.(a)
Sol. Copper shading are provided on the central limb of the shunt magnet to make the phase angle displacement between magnetic field set up by shunt magnet and supply voltage Approx. 90°

S6. Ans.(b)
Sol. Given:
⇒ (d^2 c(t))/(dt^2 ) + 4(dc(t))/dt + 5c(t) = 0
Taking Laplace Transform of the given equation, we get
⇒ s^2C(s) + 4sC(s) + 5C(s) = 0
⇒ (s^2 + 4s + 5) C(s) = 0
Comparing with the standard equation s^2+2sζω_n+ω_n^2 = 0, we get
(i) ω_n^2 = 5
⇒ ω_n = √5
(ii) 2ζω_n = 4
⇒ ζ√5 = 2
⇒ ζ = 2/√5 < 1
Hence, System is Underdamped.

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