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

Two-Port Networks - Topicwise GATE Questions on Network Theory (from 2003)

2003
1. The impedance parameters Z₁₁ and Z₁₂ of the two port network in figure are

Solution : https://www.youtube.com/watch?v=v16OcXXl_8E

2004
2. For the lattice circuit shown in figure, Z_a = j2Ω and Z_b = 2Ω. The values of the open circuit impedance parameters (Z-parameters) are

Solution : https://www.youtube.com/watch?v=Vn-O5Ll3CwU

2005
3. The ABCD parameters of an ideal n:1 transformer shown in figure are given below. The value of 'x' will be

a) n
b) 1/n
c) n²
d) 1/n²

Solution : https://www.youtube.com/watch?v=wjvAb6BEi9o

4. The h-parameters of the circuit shown in figure are

Solution : https://www.youtube.com/watch?v=lI92Vfd0F1o

2006
5. A two port network is represented by ABCD parameters as shown below. If port-2 is terminated by R_L, the input impedance seen at port-1 is given by

Solution : https://www.youtube.com/watch?v=-emJQU9Qsx8

6. In the two port network shown in the figure below, Z₁₂ and Z₂₁ are respectively

Solution : https://www.youtube.com/watch?v=JFOPiiE7frs

2008
Statement for Linked Answer Questions: 7 & 8
A two port network shown below is excited by external DC sources. The voltages and the currents are measured with voltmeters V₁, V₂ and ammeters A₁, A₂ (all assumed to be ideal), as indicated. Under following switch conditions, the readings obtained are:

7. The Z-parameter matrix for this network is

8. The h-parameter network for this network is

Solution (7 & 8): https://www.youtube.com/watch?v=_-paorTBZZg

2010
9. For the two-port network shown below, the short-circuit admittance parameter matrix is

Solution : https://www.youtube.com/watch?v=IGYPN1wEH2I

2011
10. In the circuit shown below, the network N is described by the following Y matrix: The voltage gain V₂/V₁ is

a) 1/90
b) - 1/90
c) - 1/99
d) - 1/11

Solution : https://www.youtube.com/watch?v=nyPW45iQq2c

2012
Common Data for Questions 11 and 12:
With 10 volts DC connected at port A in the linear nonreciprocal two-port network shown below,

the following were observed:
(i) 1Ω connected at port B draws a current of 3 amps
(ii) 2.5Ω connected at port B draws a current of 2 amps
11. With 10 volts DC connected at port A, the current drawn by 7Ω connected at port B is
a) 3/7 A
b) 5/7 A
c) 1 A
d) 9/7 A

12. For the same network, with 6 volts DC connected at port A, 1Ω connected at port B draws 7/3 amp. If 8 volts DC is connected to port A, the open circuit voltage at port B is
a) 6 V
b) 7 V
c) 8 V
d) 9 V

Solution (11 & 12): https://www.youtube.com/watch?v=ghASFX3RYBA

2014
13. In the h – parameter model of 2 – port network given in the figure shown,

the value of h₂₂ (in siemens) is _____________

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

14. For the two – port network shown in the figure,

the impedance (Z) matrix (in Ω) is

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

2015
15. The 2 – port Admittance matrix of the circuit shown is given by____________

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

16. The ABCD parameters of the following 2 – port network are

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

Transient Analysis of AC and DC circuits - Topicwise GATE Questions on Network Theory (from 2003)

2003
Common circuit for Questions 1 & 2:
Assume that the switch S is in position 1 for a long time and thrown to position 2 at t=0.

1. At t = 0⁺, the current i₁ is
a) – V/2R
b) – V/R
c) – V/4R
d) Zero

2. I₁(s) and I₂(s) are the Laplace Transforms of i₁(t) and i₂(t) respectively. The equations for the loop currents I₁(s) and I₂(s) for the same circuit shown, after the switch is brought from position 1 to position 2 at t = 0, are

Solution (1 & 2): https://www.youtube.com/watch?v=IiAPEkdgqQQ

2008
3. In the following cirucit, the switch S is closed at t = 0. The rate of change of current di(0⁺)/dt is given by

Solution : https://www.youtube.com/watch?v=WiYzbTZyhi0

2009
4. The switch in the circuit shown was on position 'a' for a long time, and is moved to position 'b' at time t=0. The current i(t) for t > 0 is given by

Solution : https://www.youtube.com/watch?v=ptI9Yzy17OQ

2010
5. In the cirucit shown, the switch S is open for a long time and is closed at t = 0. The current i(t) for t ≥ 0⁺ is

Solution : https://www.youtube.com/watch?v=1oztLmwhBL0

2011
6. In the circuit shown below, the initial charge on the capacitor is 2.5 mC, with the voltage polarity as indicated. The switch is closed at time t = 0. The current i(t) at a time t after the switch is closed is

Solution : https://www.youtube.com/watch?v=hQdNpuDt3zU

2014
7. In the figure shown, the ideal switch has been open for a long time.

If it is closed at t = 0, then the magnitude of the current (in mA) through the 4 kΩ resistor at t = 0⁺ is ____________

Solution : https://www.youtube.com/watch?v=lr0Teo6g4nA

2015
8. In the circuit shown, the switch SW is thrown from position A to position B at time t=0. The energy (in µJ) taken from the 3 volts source to charge the 0.1 µF capacitor from 0 volts to 3 volts is

a) 0.3
b) 0.45
c) 0.9
d) 3

Solution : https://www.youtube.com/watch?v=ZbFt7Lkclp8

9. In the circuit shown, switch SW is closed at t =0. Assuming zero initial conditions, the value of V_c(t) (in volts) at t = 1 sec is __________________

Solution : https://www.youtube.com/watch?v=_hcH81bC-cg

AC analysis of RC, RL and RLC circuits - Topicwise GATE Questions on Network Theory (from 2003)

2003
1. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q = 100. If each R, L and C is doubled from its original value, the new Q-factor of the circuit is
a) 25
b) 50
c) 100
d) 200

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

2. The differential equation for the current i(t) in the circuit shown is

Solution : https://www.youtube.com/watch?v=o3XhO6h9PhQ

3. The current flowing through the resistance R in the circuit shown has the form Pcos4t, where p is

a) (0.18 + j0.72)
b) (0.46 + j1.90)
c) - (0.18 + j1.90)
d) - (0.192 + j0.144)

Answer: Data is insufficient as inductor values are not given in the figure.

4. An input voltage v(t) = 10√2 cos(t+10^o)+ 10√3 cos(2t+10^o) volts is applied to a series combination of resistance R = 1Ω and an inductance L = 1H. The resulting steady state current i(t) in amperes is

Solution : https://www.youtube.com/watch?v=n5soJALqqaw

2004
5. The circuit shown in figure, has R = 1/3 Ω, L = 1/4 H, C = 3 F has input voltage v(t) = sin2t. The resulting current i(t) is

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

6. For the circuit shown, the time constant RC = 1 ms. The input voltage is v_i(t) = √2 sin10³t. The output voltage v_o(t) is equal to

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

7. For the R-L circuit shown, the input voltage v_i(t) = u(t). The current i(t) is

Solution : https://www.youtube.com/watch?v=OFlCLWEvc2U

8. The circuit shown in figure has initial current i_L(0^-) = 1 A through the inductor and an initial voltage V_c(0^-) = - 1 volt across the capacitor. For input v(t) = u(t), the Laplace transform of the current i(t) for t ≥ 0 is

Solution : https://www.youtube.com/watch?v=Xa5N6PQTPLs

2005
9. A square pulse of 3 volts amplitude is applied to RC circuit shown in figure. The capacitor is initially uncharged. The output voltage V_o at time t = 2 sec is

a) 3 V
b) -3 V
c) 4 V
d) -4 V

Solution : https://www.youtube.com/watch?v=lCb51w-rL_g

2006
10. In the figure shown below, assume that all the capacitors are initially uncharged. If V_i(t) = 10 u(t) volts, then V_o(t) is given by

Solution : https://www.youtube.com/watch?v=oA-NdSmNq1c

2007
11. The RC circuit shown in the figure is a

a) Low Pass Filter
b) High Pass Filter
c) Band Pass Filter
d) Band Reject Filter

Solution : https://www.youtube.com/watch?v=0f9FRURijpw

12. Two series resonant filters are as shown in the figure. Let the 3-dB bandwidth of filter 1 is B₁ and that of Filter 2 is B₂. The value of B₁/B₂ is

a) 4
b) 1
c) 1/2
d) 1/4

Solution : https://www.youtube.com/watch?v=lMKem0ESd64

13. In the circuit shown, V_c is 0 volts at t = 0 sec. For t > 0, the capacitor current i_c(t), where t is in seconds, is given by

Solution : https://www.youtube.com/watch?v=U9lh2d-zwTg

2008
14. The driving point impedance of the following network is given as shown. The component values are

Solution : https://www.youtube.com/watch?v=CI2Na_stYRg

Common Data Questions: 15 & 16
The following series RLC circuit with zero initial conditions is excited by a unit impulse function δ(t).

15. For t > 0, the output voltage V_c(t) is

Solution : https://www.youtube.com/watch?v=DB4jmdoaFIk

16. For t > 0, the voltage across the resistor is

Solution : https://www.youtube.com/watch?v=nn6PggFjKgA

2009
17. The time domain behaviour of an RL circuit is represented as shown below. For an initial current of i(0) = V_o/R, the steady state value of the current is given by

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

2010

18. For parallel RLC circuit, which one of the following statements is NOT correct?
a) The bandwidth of the circuit decreases if R is increased
b) The bandwidth of the circuit remains same if L is increased
c) At resonance, input impedance is a real quantity
d) At resonance, the magnitude of input impedance attains its minimum value.

Solution : https://www.youtube.com/watch?v=wPSqMuj0YhY

2011
19. The circuit shown below is driven by a sinusoidal input V_i = V_pcos(t/RC). The steady state output V_o is

Solution : https://www.youtube.com/watch?v=51KGart3zsQ

20. In the circuit shown below, the initial charge on the capacitor is 2.5 mC, with the voltage polarity as indicated. The switch is closed at time t = 0. The current i(t) at a time t after the switch is closed is

Solution : https://www.youtube.com/watch?v=hQdNpuDt3zU

2013
21. The transfer function V₂(s)/V₁(s) of the circuit shown below is

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

2014
22. A periodic variable x is shown in the figure as a function of time.

The root-mean-square (rms) value of x is _________________

Solution : https://www.youtube.com/watch?v=7v7xe71hIos

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

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

24. A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1H, 1F and 1Ω respectively, then the operating angular frequency (in rad/sec) is ____________________

Solution : https://www.youtube.com/watch?v=qJluHG5_mmk

25. In the figure shown, the capacitor is initially uncharged.

Which one of the following expressions describes the current I(t) in mA for t > 0 ?

Solution : https://www.youtube.com/watch?v=KRDH7b0xQNc

26. A series RC circuit is connected to a DC voltage source at time t = 0. The relation between the source voltage V_S, the resistance R, the capacitance C and the current i(t) is given below. Which one of the following represents the current i(t) ?

Solution : https://www.youtube.com/watch?v=kqPA3ph-4Lw

27. Consider the building block called 'Network N' shown in the figure. Let C = 100 µF and R = 10 kΩ.

Two such blocks are connected in cascade, as shown in the figure,

find the transfer function V₃(s)/V₁(s) of the cascaded network is

Solution : https://www.youtube.com/watch?v=kzKMHQ1Fbd4

28. 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

2015
29. In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in volts) across the capacitor is ____________________

Solution : https://www.youtube.com/watch?v=YZq-lDiqadg

30. In the circuit shown, switch SW is closed at t =0. Assuming zero initial conditions, the value of V_c(t) (in volts) at t = 1 sec is __________________

Solution : https://www.youtube.com/watch?v=_hcH81bC-cg

31. 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

32. In the circuit shown, the average value of the voltage V_ab (in volts) in steady state condition is _________

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

33. The voltage (V_c) across the capacitor (in volts) in the network shown is ______________

Solution : https://www.youtube.com/watch?v=BiEeuX6a218

34. An LC tank circuit consists of an ideal capacitor C connected in parallel with a coil of inductance L having an internal resistance R. The resonant frequency of the tank circuit is

Solution : https://www.youtube.com/watch?v=Y331K9dgrPs

35. In the circuit shown, the initial voltages across the capacitors C₁ and C₂ are 1 volt and 3 volts respectively. The switch is closed at time t = 0. The total energy dissipated (in Joules) in the resistor R until steady state is reached, is _______________

Solution : https://www.youtube.com/watch?v=wj9gkVjceEk

36. At High frequencies, the peak output voltage V_o (in volts) is __________

Solution : https://www.youtube.com/watch?v=_O4UfZGA87c

37. In the circuit shown, assume that the diodes D₁ and D₂ are ideal. The average voltage V_ab (in volts) across terminals a and b is _____________

Solution : https://www.youtube.com/watch?v=nK21y4c_m0Q

38. In the circuit shown, the current I flowing through the 50 Ω resistor will be zero, if the value of the capacitor C (in µF) is __________________

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

Two-Port Networks - Topicwise GATE Questions on Network Theory (from 2003)

Transient Analysis of AC and DC circuits - Topicwise GATE Questions on Network Theory (from 2003)

AC analysis of RC, RL and RLC circuits - Topicwise GATE Questions on Network Theory (from 2003)

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