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Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

Q1: The voltage v(t) across the terminals a and b as shown in the figure, is a sinusoidal voltage having a frequency ω = 100 radian/s. When the inductor current i(t) is in phase with the voltage v(t), the magnitude of the impedance Z (in Ω) seen between the terminals a and b is ________ (up to 2 decimal places).        (2018)
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 25
(b) 50
(c) 100
(d) 150
Ans:
(b)
Sol: At resonance imaginary part of Zeq = 0
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q2: A DC voltage source is connected to a series L-C circuit by turning on the switch S at time t = 0 as shown in the figure. Assume i(0) = 0, v(0) = 0. Which one of the following circular loci represents the plot of i(t) versus v(t) ?      (2018)
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(b) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(c) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)

(d) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Ans: (b)
Sol: Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q3: In the balanced 3-phase, 50 Hz, circuit shown below, the value of inductance (L) is 10 mH. The value of the capacitance (C) for which all the line currents are zero, in millifarads, is ___________.     (SET-2 (2016))
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 1.32
(b) 2.12
(c) 3.03
(d) 4.08
Ans:
(c)
Sol: Usingstar to delta conversion,
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Line current will be zero when the parallel pair of induction capacitor is resonant at f = 50Hz
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Since, L = 10mH
C will be 3.03 mF.

Q4: The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the admittance of the circuit becomes a pure conductance at all frequencies is _____________.       (SET-1  (2016))
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 14.14
(b) 8.62
(c) 22.46
(d) 12.18
Ans:
(a)
Sol: The resonant frequency for the circuit is
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)So the circuit will have zero real part of admittance when,
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q5: An inductor is connected in parallel with a capacitor as shown in the figure.
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)As the frequency of current i is increased, the impedance (Z) of the network varies as       (SET-1 (2015))
(a) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(b) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(c) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(d) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Ans: 
(b)
Sol: Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q6: A series RLC circuit is observed at two frequencies. At ω1 = 1 krad/s, we note that source voltage V1 = 100∠0° V results in a current  I= 0.03∠31°A. At ω= 2 krad/s, the source voltage V= 100∠0° V results in a current I2 = 2∠0. The closest values for R, L, C out of the following options are        (SET-3 (2014))
(a) R = 50 Ω ; L = 25mH; C = 10 μ F;
(b) R = 50 Ω ; L = 10 mH; C = 25 μ F;
(c) R = 50 Ω ; L = 50 mH; C = 5 μ F;
(d) R = 50 Ω ; L = 5mH; C = 50 μ F;
Ans:
(b)
Sol: Given
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)At ω2 = 2k rad/s, voltage and current are in phase. Thus, it is a case of series resonance,
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)∴ Resistance of circuit,
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Comparing equation (i) and (ii), we have:
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)From equation (iii),
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Substituting the value of C in equation (iv), we get,
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Therefore, values are:
𝑅=50Ω,R = 50Ω,
L=10mH,
C = 25μF  

Q7: Two magnetically uncoupled inductive coils have Q factors qand q2 at the chosen operating frequency. Their respective resistances are R1 and R2. When connected in series, their effective Q factor at the same operating frequency is        (2013)
(a) 𝑞1𝑅1+𝑞2𝑅2q1R1 + q2R2
(b) (𝑞1/𝑅1)+(𝑞2/𝑅2)(q1/R1) + (q2/R2)
(c) (𝑞1𝑅1+𝑞2𝑅2)/(𝑅1+𝑅2)(q1R1 + q2R2)/(R1 + R2)  
(d) 𝑞1𝑅2+𝑞2𝑅1q1R+ q2R
Ans: 
(c)
Sol: Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q8: The resonant frequency for the given circuit will be    (2008)
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 1 rad/s
(b) 2 rad/s
(c) 3 rad/s
(d) 4 rad/s
Ans:
(c)
Sol: Input impedance
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)At resonance, imaginary part must be zero.
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q9: In the figure given below all phasors are with reference to the potential at point "O". The locus of voltage phasor VXY as R is varied from zero to infinity is shown by     (2007)
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(b) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(c) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(d) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Ans:
(a)
Sol: Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Let, capacitive reactance = XC
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Using KVL,
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Method-1:
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)When R = 0
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Method-2:
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Magnitude of VYX  = V
So, option (C) and (D) can not be correct, as magnitude is 2 V in these two options.
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)on the basis of above analysis, the locus of VYX is drawn below:
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q10: The R-L-C series circuit shown in figure is supplied from a variable frequency voltage source. The admittance-locus of the R-L-C network at terminals AB for increasing frequency ω is       (2007)
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(b) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(c) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(d) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Ans: 
(d)
Sol: Admittance of the series connected RLC
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Separating, real and imaginary part of admittance.
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)For any value of ω , the real part is always positive. When,
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Imaginary part of zero
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)On the basis of above analysis, the admittance locus is
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q11:The circuit shown in the figure is energized by a sinusoidal voltage source V1 at a frequency which causes resonance with a current of I.
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)The phasor diagram which is applicable to this circuit is      (2006)
(a) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(b) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(c) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(d) Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Ans:
(a)
Sol: Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)At resonance,
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Therefore, input impedance in purely resistive, is minimum, and the input voltage and output current are in phase.
So, V1 and I are in phase
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)But, XL = XC
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Therefore, V2 is in phase with V1 and V< V1 voltage across the capacitor
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)So, VC lags the current by 90.
The phasor diagram on the basis of above analysis.
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q12: The value of Z in figure, which is most appropriate to cause parallel resonance at 500 Hz is      (2004)
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 125.00 mH
(b)304.20 μF
(c) 2.0 μF
(d) 0.05 μF
Ans: 
(d)
Sol: Atresonance, the circuit should be in unity power factor.
Hence, 'Z' should be capacitive.
Admittance of the parallel circuit.
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q13: In the circuit of figure, the magnitudes of VL and VC are twice that of VR. Given that f = 50 Hz, the inductance of the coil is      (2003)
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 2.14 mH
(b) 5.30 H
(c) 31.8 mH
(d) 1.32 H
Ans:
(c)
Sol: Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Therefore, the circuit is at resonance and
VR = V
 Quality factor Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)As we know,
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q14: A series R-L-C circuit has R = 50Ω, L = 100μ and C = 1μ. The lower half power frequency of the circuit is       (2002)
(a) 30.55 kHz
(b) 3.055 kHz
(c) 51.92 kHz
(d) 1.92 kHz
Ans: 
(b)
Sol: Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q15: In the circuit shown in figure, what value of C will cause a unity power factor at the ac source?      (2002)
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 68.1 μF
(b) 165 μF
(c) 0.681𝜇𝐹0.681 μF
(d) 6.81 μF
Ans:
(a)
Sol: Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)To have unity power factor at ac source i.e. resonance condition,
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q16: In a series RLC circuit at resonance, the magnitude of the voltage developed across the capacitor     (2001)
(a) is always zero
(b) can never be greater than the input voltage
(c) can be greater than the input voltage, however, it is 90 out of phase with the input voltage
(d) can be greater than the input voltage, and is in phase with the input voltage.
Ans:
(c)
Sol: In a series RLC circuit, at resonance
Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE)Hence, option (C) is correct.

The document Previous Year Questions- Resonance and Locus Diagrams | Network Theory (Electric Circuits) - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Network Theory (Electric Circuits).
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FAQs on Previous Year Questions- Resonance and Locus Diagrams - Network Theory (Electric Circuits) - Electrical Engineering (EE)

1. What is resonance in electrical circuits?
Ans. Resonance in electrical circuits occurs when the inductive reactance and capacitive reactance cancel each other out, resulting in a frequency at which the circuit is most efficient in storing and transferring energy.
2. How do resonance and frequency relate to each other in a circuit?
Ans. In a circuit, resonance occurs at a specific frequency where the inductive and capacitive reactances are equal and cancel each other out, resulting in maximum current flow and energy transfer.
3. What are the applications of resonance in electrical circuits?
Ans. Resonance in electrical circuits is utilized in applications such as tuning radio receivers, designing filters, and improving power factor correction in power systems.
4. How do resonance diagrams help in understanding circuit behavior?
Ans. Resonance diagrams, also known as locus diagrams, visually represent how the impedance of a circuit changes with frequency, helping to identify resonant frequencies and understand the behavior of the circuit.
5. How can one calculate the resonant frequency of a circuit?
Ans. The resonant frequency of a circuit can be calculated using the formula f = 1/(2π√(LC)), where f is the resonant frequency, L is the inductance, and C is the capacitance in the circuit.
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