GATE 2023 - Important Concepts, Short cuts, Complete Solutions, Examples and Practice Problems

Network Theorems (Thevenin's, Superposition, Maximum Power Transfer etc...) - Topicwise GATE Questions on Network Theory (from 2003))

2003
1. A source of angular frequency 1 rad/sec has source impedance consisting of 1 Ω resistance in series with 1 H inductance. The load that will obtain the maximum power transfer is
a) 1 Ω resistance
b) 1 Ω resistance in parallel with 1 H inductance
c) 1 Ω resistance in series with 1 F capacitor
d) 1 Ω resistance in parallel with 1 F capacitor

Solution : https://www.youtube.com/watch?v=UH5csZbXYgc

2005
2. The maximum power that can be transferred to the load resistor R_L form the voltage source in figure is

a) 1 W
b) 10 W
c) 0.25 W
d) 0.5 W

Solution : https://www.youtube.com/watch?v=IW9o-PZYI6E

3. For the circuit shown in figure, Thevenin's voltage and Thevenin's equivalent resistance at terminals a-b is

a) 5 V and 2 Ω
b) 7.5 V and 2.5 Ω
c) 4 V and 2 Ω
d) 3 V and 2.5 Ω

Solution : https://www.youtube.com/watch?v=wlcChf7gBWE

2007
4. An independent voltage source in series with an impedance Z_s = R_s + j X_s delivers a maximum average power to a load impedance Z_L when
a) Z_L = R_s + jX_s
b) Z_L = R_s
c) Z_L = jX_s
d) Z_L = R_s - jX_s

Solution : https://www.youtube.com/watch?v=o9Awvha9eAg

5. For the circuit shown in the figure, the Thevenin's voltage and resistance looking into X-Y are

a) 4/3 volts. 2 Ω
b) 4 volts. 2/3 Ω
c) 4/3 volts. 2/3 Ω
d) 4/ volts. 2 Ω

Solution : https://www.youtube.com/watch?v=M9_ZDSgAKLI

2008
6. The Thevenin’s equivalent impedance Z_TH between the nodes P and Q in the following circuit is

Solution : https://www.youtube.com/watch?v=vl6exaG9eY0

2009
7. An AC source of RMS voltage 20 volts with internal impedance Z_i = (1+2j) Ω feeds a load of impedance Z_L = (7+4j) Ω in the figure below. The reactive power consumed by the load is

a) 8 VAR
b) 16 VAR
c) 28 VAR
d) 32 VAR

Solution : https://www.youtube.com/watch?v=w36Rox8j0KA

8. In the circuit shown, what value of R_L maximizes the power delivered to R_L?

a) 2.4 Ω
b) 8/3 Ω
c) 4 Ω
d) 6 Ω

Solution : https://www.youtube.com/watch?v=yqt0czRs6_I

2011
9. In the circuit shown below, find the value of R_L such that the power transferred to R_L is maximum.

a) 5 ohms
b) 10 ohms
c) 15 ohms
d) 20 ohms

Solution : https://www.youtube.com/watch?v=PIWsYGVUf0o

2012
10. The average power delivered to an impedance (4-j3)Ω by a current 5cos(100πt+100) Amp is
a) 44.2 W
b) 50 W
c) 62.5 W
d) 125 W

Solution : https://www.youtube.com/watch?v=WMAyaRN-XxU

11. The impedance looking into nodes 1 and 2 in the given circuit is

a) 50 Ω
b) 100 Ω
c) 5 kΩ
d) 10.1 kΩ

Solution : https://www.youtube.com/watch?v=M7px_ck8xa4

12. Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

a) 0.8 Ω
b) 1.4 Ω
c) 2 Ω
d) 2.8 Ω

Solution : https://www.youtube.com/watch?v=RYUCtIAHMkE

2013
13. A source V_s(t) = V cos100πt has an internal impedance of (4 + j3) Ω. If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in Ω should be
a) 3
b) 4
c) 5
d) 7

Solution : https://www.youtube.com/watch?v=_a3PEIDOI08

14. In the circuit shown below, if the source voltage V_s = 100∟53.13^o volts then the thevenin's equivalent voltage in volts as seen by the load resistance R_L is

Solution : https://www.youtube.com/watch?v=XnD2y6tMyFM

2014
15. For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance Z₁ of the first section to the input impedance Z₂ of the second section is
a) Z₂ = Z₁
b) Z₂ = – Z₁
c) Z₂ = Z₁^*
d) Z₂ = – Z₁^*

Solution : https://www.youtube.com/watch?v=vK_w7K2D-9M

16. A 230 volts rms source supplies power to two loads connected in parallel. The first load draws 10kW at 0.8 leading power factor and the second one draws 10 kVA at 0.8 lagging power factor. The complex power delivered by the source is
a) (18 + j 1.5) kVA
b) (18 – j 1.5) kVA
c) (20 + j 1.5) kVA
d) (20 – j 1.5) kVA

Solution : https://www.youtube.com/watch?v=XF8e5rYmmm8

17. Norton's theorem states that a complex network connected to a load can be replaced with an equivalence impedance
a) in series with a current source
b) in parallel with a voltage source
c) in series with a voltage source
d) in parallel with a current source

Solution : https://www.youtube.com/watch?v=z8p5iNyHA60

18. In the circuit shown in the figure, the angular frequency ω (in rad/sec), at which the Norton equivalent impedance as seen from terminals b – b' is purely resistive, is _____________

Solution : https://www.youtube.com/watch?v=doL-VE7tziY

19. The equivalent resistance in the infinite ladder network shown in the figure is R_e.

The value of R_e/R is ________________

Solution : https://www.youtube.com/watch?v=UeUdAyWscyI
2015

20. In the given circuit, the maximum power (in Watts) that can be transferred to the load R_L is _______

Solution : https://www.youtube.com/watch?v=Hr4AS712hRM

21. In the circuit shown, the Norton equivalent resistance (in Ω) across terminals a and b is ________

Solution : https://www.youtube.com/watch?v=w8z1zeVVm1c

22. For the current shown in the figure, the Thevenin’s equivalent voltage (in volts) across terminals a and b is _______________

Solution : https://www.youtube.com/watch?v=JNhFCs7jQiM

KVL, KCL, Mesh & Nodal Analysis, Power and Energy Calculations - Topicwise GATE Questions on Network Theroy (from 2003)

2003
1. The minimum number of equations required to analyze the circuit shown in figure is

a) 3
b) 4
c) 6
d) 7

Solution : https://www.youtube.com/watch?v=_E2r6haGMdw

2. Twelve 1Ω resistances are used to form a cube. The resistance between two diagonally opposite corners of the cube is
a) 5/6 Ω
b) 1/6 Ω
c) 6/5 Ω
d) 3/2 Ω

Solution : https://www.youtube.com/watch?v=DRvJzaE6cqM

2005
3. If R₁ = R₂ = R₄ = R and R₃ = 1.1R in the bridge circuit shown in figure, then the reading in the ideal voltmeter connected between a and b is

a) 0.238 V
b) 0.138 V
c) - 0.238 V
d) 1 V

Solution : https://www.youtube.com/watch?v=NEqaefUlYLc

2006
4. A 2 mH inductor with some initial current can be represented as shown below, where 's' is the Laplace Transform variable. The value of initial current is :

a) 0.5 A
b) 2.0 A
c) 1.0 A
d) 0.0 A

Solution : https://www.youtube.com/watch?v=145BHvtN10o

2009
5. A fully charged mobile phone with a 12 volts battery is good for a 10 min talk time.

Assume that, during the talk time, the battery delivers a constant current of 2 Amp and its voltage drops linearly from 12 volts to 10 volts as shown in the figure. How much energy does the battery deliver during this talk-time?
a) 220 J
b) 12 kJ
c) 13.2 kJ
d) 14.4 kJ

Solution : https://www.youtube.com/watch?v=GV1gFYMN_wc

6. In the interconnection of ideal sources shown in figure, it is known that the 60 volts source is absorbing power. Which of the following can be the value of the current source I?

a) 10 A
b) 13 A
c) 15 A
d) 18 A

Solution : https://www.youtube.com/watch?v=2mwLjmGEWzo

2010
7. In the circuit shown, the power supplied by the voltage source is

a) 0 W
b) 5 W
c) 10 W
d) 100 W

Solution : https://www.youtube.com/watch?v=hibsYBmkeSw

2012
8. In the following figure, C₁ and C₂ are ideal capacitors. C₁ has been charged to 12 volts before the ideal switch S is closed at t = 0. The current i(t) for all t is

a) zero
b) a step function
c) an exponentially decaying function
d) an impulse function

Solution : https://www.youtube.com/watch?v=TQNMvTneDBQ

9. If V_A - V_B = 6 volts, then V_C - V_D is

a) - 5 volts
b) 2 volts
c) 3 volts
d) 6 volts

Solution : https://www.youtube.com/watch?v=IXotTdO6ABw

2013
10. Consider a delta connection of resistors and its equivalent star connection as shown below.

If all elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding star equivalent will be scaled by a factor of
a) k²
b) k
c) 1/k
d) √k

Solution : https://www.youtube.com/watch?v=DZotuMVh2vQ

11. Three capacitors C₁, C₂ and C₃ whose values are 10 µF, 5 µF and 2 µF respectively, have breakdown voltages of 10, 5 and 2 volts respectively.

For the interconnection shown below, the maximum safe voltage in volts that can be applied across the combination, and the corresponding total charge in µC stored in the effective capacitance across the terminals are respectively.
a) 2.8 and 3.6
b) 7 and 119
c) 2.8 and 36
d) 7 and 80

Solution : https://www.youtube.com/watch?v=9bRJQhA6s3A

Common Data for Questions 12 and 13:
consider the figure shown below

12. The current I_S in Amps in the voltage source, and the voltage V_S in volts across the current source respectively are
a) 13, - 20
b) 8, - 10
c) - 8, 20
d) - 13, 20

13. The current in the 1 Ω resistor in Amps is
a) 2
b) 3.33
c) 10
d) 12

Solution (12 & 13): https://www.youtube.com/watch?v=ABDbciYDFQY

2014
15. Consider the configuration shown in the figure, which is a portion of a larger electrical network. For R = 1 Ω and currents i₁ = 2A, i₄ = – 1A, i₅ = – 4A, which one of the follwoing is TRUE?

a) i₆ = 5 A
b) i₃ = – 4 A
c) Data is sufficient to conclude that the supposed currents are impossible
d) Data is insufficient to identify the currents i₂, i₃ and i₆

Solution : https://www.youtube.com/watch?v=6V2OJEMgW5w

16. A Y– network has resistances of 10 Ω each in two of its arms, while the third arm has a resistance of 11Ω. In the equivalent Δ – network, the lowest value (in Ω) among the three resistances is _________

Solution : https://www.youtube.com/watch?v=ARDUJZE9iaY

17. In the figure shown, the value of the current I (in Amperes) is ______________

Solution : https://www.youtube.com/watch?v=q-BiYlq1ZC4

18. For the Y – network shown in the figure, the value of R₁ (in Ω) in the equivalent Δ – network is ____

Solution : https://www.youtube.com/watch?v=bp_eya6DnwA

19. The circuit shown in the figure represents a

a) Voltage controlled voltage source
b) voltage controlled current source
c) current controlled current source
d) current controlled voltage source

Solution : https://www.youtube.com/watch?v=GmSi1BWeOjA

20. The magnitude of current (in mA) through the resistor R₂ in the figure shown is ___________

Solution : https://www.youtube.com/watch?v=I6Gnn4ZdNLY

23. The equivalent resistance in the infinite ladder network shown in the figure is R_e.

The value of R_e/R is ________________

Solution : https://www.youtube.com/watch?v=UeUdAyWscyI

2015
21. In the network shown in the figure, all resistors are identical with R = 300 Ω. The resistance R_ab (in Ω) of the network is __________________

Solution : https://www.youtube.com/watch?v=R2Lsmws8L2U

22. In the given circuit, the values of V₁ and V₂ (in volts) respectively are

a) 5, 25
b) 10, 30
c) 15, 35
d) 0, 20

Solution : https://www.youtube.com/watch?v=0YY9dEZPVUI

23. In the circuit shown, the voltage V_x (in volts) is __________

Solution : https://www.youtube.com/watch?v=nfrqvps0ojs

Time Response & Transfer Function of a System - Topic wise GATE Questions on Control Systems (from 2003)

2003
1. The driving point impedance Z(s) of a network has the pole-zero locations as shown in figure. If Z(0) = 3, then Z(s) is

Solution : https://www.youtube.com/watch?v=VkjfxpWTPj4

2. A second order system has the transfer function C(s)/R(s) = 4 / [s² + 4s + 4] with r(t) as the unit step function, the response c(t) of the system is represented by

Solution : https://www.youtube.com/watch?v=-G7mdzB-60I

2004
3. The transfer function H(s) of an RLC circuit is given as 10⁶/[s²+20s+10⁶], then the Q – factor of this circuit is
a) 25
b) 50
c) 100
d) 5000

Solution : https://www.youtube.com/watch?v=uyZ1HtXU6Ow

4. For the circuit shown in figure, the initial conditions are zero. Its transfer function V_o(t)/V_i(t) is

Solution : https://www.youtube.com/watch?v=JKzEzWRjN4Q

2005
5. In the derivation of expression for peak percent overshoot, which one of the following conditions is NOT required?
a) system is linear and time invariant
b) system transfer function has a pair of complex conjugate poles and no zeros
c) there is no transportation delay in the system
d) the system has zero initial conditions

Solution : https://www.youtube.com/watch?v=CCM2Ygcsj1s

6. A double integrator plant, G(s) = K/S², H(s) = 1 is to be compensated to achieve the damping ratio ξ = 0.5, and an undamped natural frequency ω_n = 5 rad/sec. Which one of the following compensator G_c(s) will be suitable?

Solution : https://www.youtube.com/watch?v=5FCT5oDsBf0

2006
7. The unit step response of a system starting from rest is given by c(t) = 1 – e^–2t for t ≥ 0. The transfer function of the system is
a) 1 / (1 + 2s)
b) 2 / (2 + s)
c) 1 / (2 + s)
d) 2s / (1 + 2s)

Solution : https://www.youtube.com/watch?v=KvqQF5J_bgY

8. The unit impulse response of a system is h(t) = e^–t, t ≥ 0. For this system, the steady state value of the output for unit step input is equal to
a) –1
b) 0
c) 1
d) ∞

Solution : https://www.youtube.com/watch?v=8jfSroqXbV8

2007
9. If the closed loop transfer function of a control system is given as T(s) = (s – 5)/[(s + 2)(s + 3)], then it is
a) an unstable system
b) an uncontrollable system
c) a minimum phase system
d) a non-minimum phase system

Solution : https://www.youtube.com/watch?v=4soEmuGvfcI

10. The transfer function of a plant is T(s) = 5/[(s + 5)(s² + s + 1)]. The second order approximation of T(s) using dominant pole concept is

Solution : https://www.youtube.com/watch?v=y1BxLLTHJOI

2008
11. The pole-zero plot given below corresponds to a

a) Low pass filter
b) High pass filter
c) band pass filter
d) Notch filter

Solution : https://www.youtube.com/watch?v=ZaDLLdETZPs

12. Step response of a set of three second order under damped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?

Solution : https://www.youtube.com/watch?v=X0RUYGCL8P4

13. Group – I lists a set of four transfer functions. Group – II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions.

a) P - 3, Q - 1, R - 4, S - 2
b) P - 3, Q - 2, R - 4, S - 1
c) P - 2, Q - 1, R - 4, S - 3
d) P - 3, Q - 4, R - 1, S – 2

Solution : https://www.youtube.com/watch?v=jXGZriqlb1c

14. A certain system has transfer function G(s) = (s + 8)/(s² + αs – 4 ), where α is a parameter. Consider the standard negative unity feedback configuration shown below.

Which of the following statements is true?
a) The closed loop system is never stable for any value of α
b) For some positive values of α, the closed loop system is stable, but not for all positive values
c) For all positive values of α, the closed loop system is stable
d) The closed loop system is stable for all values of α, both positive and negative

Solution : https://www.youtube.com/watch?v=lgA_id_ATbY

15. The magnitude of frequency response of an under damped second order system is 5 at 0 rad/sec and peaks to 10/√3 at 5√2 rad/sec. The transfer function of the system is

Solution : https://www.youtube.com/watch?v=3a4n-8XUFCg

2009
16. If the transfer function of the following circuit is V_o(s)/V_i(s) = 1/(2+sCR), then the value of the load resistor R_L is

a) R/4
b) R/2
c) R
d) 2R

Solution : https://www.youtube.com/watch?v=0bJX_BCy6bc

2010
17. The transfer function Y(s)/R(s) of the system shown is

Solution : https://www.youtube.com/watch?v=ORTP8lmNl44

18. A system with transfer function Y(s)/X(s) = s/(s + p) has an output y(t) = cos(2t – π/3) for the input signal x(t) = p cos(2t – π/2). Then, the system parameter 'p' is
a) √3
b) 2/√3
c) 1
d) √3/2

Solution : https://www.youtube.com/watch?v=3WAIkGRRes4

2011
19. The differential equation 100d²y/dt²-20dy/dt+y = x(t) describes a system with an input x(t) and an output y(t).The system which is initially relaxed, is excited by a unit step input. The output y(t) can be represented by the waveform

Solution : https://www.youtube.com/watch?v=nGDKxd0P1DA

2012
20. A system with transfer function is excited by sin(ωt).

The steady state output of the system is zero at
a) ω = 1 rad/sec
b) ω = 2 rad/sec
c) ω = 3 rad/sec
d) ω = 4 rad/sec

Solution : https://www.youtube.com/watch?v=UYEEuh71lxc

2013
21. Which one of the following is NOT TRUE for a continuous time causal and stable LTI system?
a) all the poles of the system must lie on the left side of the jω axis
b) zeros of the system can lie anywhere in the s-plane
c) all the poles must lie with in |s| = 1
d) all the roots of the characteristic equation must be located on the let side of the jω axis

Solution : https://www.youtube.com/watch?v=pKt_YzAm3z0

22. A polynomial f(x) = a₄x⁴+a₃x³+a₂x²+a₁x–a₀ with all coefficients positive has
a) no real roots
b) no negative real root
c) odd number of real roots
d) at least one positive and one negative real root

Solution :

23. Assuming zero initial conditions, the response y(t) of the system given below for a unit step input, u(t) is __________________

a) u(t)
b) t.u(t)
c) (1/2)t².u(t)
d) e^-t.u(t)

Solution : https://www.youtube.com/watch?v=haTwaJVl46E

24. The transfer function V₂(s)/V₁(s) of the circuit shown is

Solution : https://www.youtube.com/watch?v=iVJ4qUlg8BE

25. The open loop transfer function of a DC motor is given as ω(s)/V_a(s) = 10/(1+10s). when connected in feedback as shown below.

The approximate value of K_a that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open loop system is
a) 1
b) 5
c) 10
d) 100

Solution : https://www.youtube.com/watch?v=594vhbYCvbs

2014
26. The forward path transfer function of a unity feedback system is given by

The value of K which will place both the poles of the closed loop system at the same location is
_________________

Solution : https://www.youtube.com/watch?v=XwzA0qsCdYs

27. In the circuit shown, the value of capacitor C (in mF) needed to have critically damped response i(t) is ______________________

Solution : https://www.youtube.com/watch?v=MTY9pmGILi4

28. For the following feedback system

The 2% settling time of the step response is required to be less than 2 seconds.
Which one of the following compensators C(s) achieves this?

Solution : https://www.youtube.com/watch?v=b-mTm3UY9Go

29. The natural frequency of an undamped second order system is 40 rad/sec. If the system is damped with a damping ratio 0.3, the damped natural frequency in rad/sec is ______________

Solution : https://www.youtube.com/watch?v=v8DCS-MhNUs

30. For the second order closed loop system shown in the figure,

the natural frequency (in rad/sec) is
a) 16
b) 4
c) 2
d) 1

Solution : https://www.youtube.com/watch?v=x0bqQ1Wbxeg

2015
31. A unity negative feedback system has an open loop transfer function G(s) = K / S(S+10), the gain K for the system to have a damping ratio of 0.25 is _____________

Solution : https://www.youtube.com/watch?v=LCcmOh0C1rY

32. The output of a standard second order system for a unit step input is given as

The transfer function of the system is

Solution : https://www.youtube.com/watch?v=gRlkHoZYDX4

Network Theorems (Thevenin's, Superposition, Maximum Power Transfer etc...) - Topicwise GATE Questions on Network Theory (from 2003))

KVL, KCL, Mesh & Nodal Analysis, Power and Energy Calculations - Topicwise GATE Questions on Network Theroy (from 2003)

Time Response & Transfer Function of a System - Topic wise GATE Questions on Control Systems (from 2003)

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