Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Notes  >  Network Theory (Electric Circuits)  >  Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters

Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

Q1: For the circuit shown in the figure, the source frequency is 5000 rad/sec. The mutual inductance between the magnetically coupled inductors is 5mH with their self inductances being 125mH and 1mH. The Thevenin's impedance. Zth, between the terminals P and Q in Ω is _____ (rounded off to 2 decimal places).       (2024)
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 5.33
(b) 4.55
(c) 6.25
(d) 7.58
Ans:
(a)
Sol: Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q2: The transfer function of a real system, H(s), is given as:
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)where A, B, C and D are positive constants. This system cannot operate as      (2022)
(a) low pass filter.
(b) high pass filter
(c) band pass filter.
(d) an integrator.
Ans:
(b, d)
Sol: Put Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)So, the system pass low frequency component. Put s = ∞, H(∞) = 0
For high pass filter, high frequency component should be non zero. Hence this system cannot be operated as high pass filter. 

Q3: An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance M between the windings of the transformer is ____________ μH.(Round off to 2 decimal places.)     (2021)
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 12.14
(b) 68.26
(c) 51.1
(d) 78.4
Ans:
(c)
Sol: Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q4: The input impedance, Zin (s) for the network shown is     (2021)
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)

(b) 6s + 4
(c) 7s + 4
(d) Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)

Ans: (a)
Sol: Circuit in s-domain,
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q5: The line currents of a three-phase four wire system are square waves with amplitude of 100 A. These three currents are phase shifted by 120°  with respect to each other. The rms value of neutral current is     (2019)
(a) 0 A
(b) Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)

(c) 100 A
(d) 300 A
Ans:
(c)
Sol: Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q6: The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is     (2018)
(a) 11
(b) 12
(c) 13
(d) 14
Ans: 
(b)
Sol: Loops = b - (N-1)
5 = b-(8-1)
b = 12

Q7: The graph associated with an electrical network has 7 branches and 5 nodes. The number of independent KCL equations and the number of independent KVL equations, respectively, are       (SET-2 (2016))
(a) 2 and 5
(b) 5 and 2
(c) 3 and 4
(d) 4 and 3
Ans:
(d)
Sol: Number of KCL equations
= n - 1 = 5 - 1 = 4
Number of KVL equations
= b - (n - 1) = 7 - (5 - 1) = 3

Q8: The following figure shows the connection of an ideal transformer with primary to secondary turns ratio of 1 : 100. The applied primary voltage is 100 V (rms), 50 Hz, AC. The rms value of the current I, in ampere, is __________.         (SET-2 (2016))
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 100
(b) 10
(c) 20
(d) 50
Ans:
(b)
Sol: The above circuit can be drown by transferring secondary circuit to primary side.Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)So the rms value of I will be 10 A.

Q9: Two identical coils each having inductance L are placed together on the same core. If an overall inductance of αL is obtained by interconnecting these two coils, the minimum value of α is ____.        (SET-2 (2015))
(a) 0
(b) 0.25
(c) 0.5
(d) 0.75
Ans:
(a)
Sol: CASE-I:
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)CASE-III
If both are diffferentially coupled then
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Minimum value = 0

Q10: Find the transformer ratios a and b such that the impedance (Zin) is resistive and equals 2.5Ω when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.       (SET-2 (2015))
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) a = 0.5, b = 2.0
(b) a = 2.0, b = 0.5
(c) a = 1.0, b = 1.0
(d) a = 4.0, b = 0.5
Ans
: b
SolPrevious Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)From equation (i) and (ii),
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q11: Two identical coupled inductors are connected in series. The measured inductances for the two possible series connections are 380 μH and 240 μH. Their mutual inductance in μH is _____.        (SET-2 (2014))
(a) 10
(b) 15
(c) 55
(d) 35
Ans: 
(d)
Sol: The two possible series connection are shown below:
Let the mutual inductance be M
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)(i) Additive connection,
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)(ii) Substractive connection,
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Solving equations (i) and (ii), we get:
4M = 140 μH
M = 35 μH
Therefore, mutual inductance M = 35μH

Q12: The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage 𝑉𝑊𝑋1VWX1 = 100 V is applied across WX to get an open circuit voltage VYZ1 across YZ. Next, an ac voltage VYZ2 = 100 V is applied across YZ to get an open circuit voltage VWX2 across WX. Then, VYZ1 / VWX1, VWX2 / VYZ2 are respectively,      (2013)
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 125/100 and 80/100
(b) 100/100 and 80/100
(c) 100/100 and 100/100
(d) 80/100 and 80/100
Ans:
(b)
Sol: VYZ1 = 100 × 1.25 × 0.8 = 100
In second case when 100 V is applied at YZ terminals, this whole 100 V will appear across the secondary winding,
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q13: The number of chords in the graph of the given circuit will be      (2008)
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) 3
(b) 4
(c) 5
(d) 6
Ans:
(a)
Sol: Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Number of branches = b = 6
No. of nodes = n = 4
No. of chords = b - (n - 1) =6 - (4 - 1) = 3

Q14: The matrix A given below in the node incidence matrix of a network. The columns correspond to branches of the network while the rows correspond to nodes. Let V= [vv... v6]T denote the vector of branch voltages while I = [ii... i6]T that of branch currents. The vector E = [e1 e2 e3 e4]denotes the vector of node voltages relative to a common ground.
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Which of the following statement is true ?      (2007)
(a) The equations v− v+ v= 0, v+ v− v= 0 are KVL equations for the network for some loops
(b) The equations v− v− v= 0, v+ v− v= 0 are KVL equations for the network for some loops
(c) E = AV
(d) AV = 0 are KVI equations for the network
Ans:
(b)
Sol: Convention:
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)(when branch bj enters node Ni)
Given node incidence matrix
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)eg.: Branch b1 enter N3 and leaves N1
The oriented network graph
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Using KVL, in loop containing branches b1, b3 and  b6
v− v− v= 0
In loop containing branches b4, b5 and b6
 v+ v− v= 0

Q15: In the circuit shown in figure, it is found that the input ac voltage (Vi) and current i are in phase. The coupling coefficient is  Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE) where M is the mutual inductance between the two coils. The value of K and the dot polarity of the coil P-Q are    (2002)
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)(a) K = 0.25 and dot at P
(b) K = 0.5 and dot at P
(c) K = 0.25 and dot at Q
(d) K = 0.5 and dot at Q
Ans:
c
Sol: Input ac voltage and current will be in phase only at resonance condition,
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Hence, coupling will be opposite.
Therefore, Dot will be at Q.

Q16: A first order, low pass filter is given with R = 50 Ω and C = 5μF. What is the frequency at which the gain of the voltage transfer function of the filter is 0.25?       (2002)
(a) 4.92 kHz
(b) 0.49 kHz
(c) 2.46 kHz
(d) 24.6 kHz
Ans: 
(c)
Sol: Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)On solving,
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Q17: The graph of an electrical network has N nodes and B branches. The number of links, L, with respect to the choice of a tree, is given by    (2002)
(a) B - N + 1
(b) B + N
(c) N - B + 1
(d) N - 2B -1
Ans:
(a)
Sol: Number of links = B - (N - 1) = B - N + 1

Q18: A connected network of N > 2 nodes has at most one branch directly connecting any pair of nodes. The graph of the network      (2001)
(a) must have at least N branches for one or more closed paths to exist
(b) can have an unlimited number of branches
(c) can only have at most N branches
(d) can have a minimum number of branches not decided by N
Ans:
(a)

Q19: Given two coupled inductors L1 and L2, their mutual inductance M satisfies      (2001)
(a) Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)

(b) Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)
(c) Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)
(d) Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)
Ans: (d)
Sol: Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)where , K= coefficient of coupling
Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | Network Theory (Electric Circuits) - Electrical Engineering (EE)

The document Previous Year Questions- Magnetically Coupled Circuits, Network Topology and Filters | 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- Magnetically Coupled Circuits, Network Topology and Filters - Network Theory (Electric Circuits) - Electrical Engineering (EE)

1. What are the different types of magnetic coupling in circuits?
Ans. The different types of magnetic coupling in circuits are mutual inductance, where two coils are magnetically coupled and induce voltage in each other, and self-inductance, where a coil induces voltage in itself due to the changing current flowing through it.
2. How does the topology of a network affect its performance?
Ans. The topology of a network determines the arrangement of nodes and connections, impacting factors like data transfer speed, reliability, and scalability. Common topologies include bus, ring, star, and mesh.
3. What are the characteristics of a low-pass filter?
Ans. A low-pass filter allows signals below a certain frequency to pass through while attenuating signals above that frequency. It is commonly used to remove high-frequency noise from a signal.
4. How does magnetic coupling help in wireless power transfer?
Ans. Magnetic coupling allows for the transfer of energy wirelessly between two coils placed near each other. The primary coil generates a magnetic field, which induces a current in the secondary coil, enabling power transfer without physical connections.
5. What is the purpose of using filters in electronic circuits?
Ans. Filters are used in electronic circuits to selectively pass or block certain frequencies of signals. They help in removing unwanted noise, shaping signal waveforms, and separating different frequency components in a signal.
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