June 2015 | GATE 2023 - Important Concepts, Short cuts, Complete Solutions, Examples and Practice Problems

GATE 2004 ECE Network Theory - Complete Video Solutions with Answers

2004
1. Consider the network graph shown in figure. Which one of the following is NOT a ‘tree’ of this group?

Solution: https://www.youtube.com/watch?v=xjHxZjJq8PI

2. The equivalent inductance measured between the terminals 1 and 2 for the circuit shown in figure, is

a) L₁ + L₂ + M
b) L₁ + L₂ - M
c) L₁ + L₂ + 2M
d) L₁ + L₂ - 2M

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

3. 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

4. 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

5. 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

6. 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

7. 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

8. Consider the following statements S1 and S2
S1: at the resonant frequency, the impedance of a series RLC circuit is zero.
S2: In a parallel G-L-C circuit, increasing the conductance G results in increase in its Q-factor.
Which one of the following is correct?
a) S1 is FALSE and S2 is TRUE
b) Both S1 and S2 are TRUE
c) S1 is TRUE and S2 is FALSE
d) Both S1 and S2 are FALSE

Solution: https://www.youtube.com/watch?v=s3hM-idhg2s

GATE 2005 ECE Network Theory - Complete Video Solutions with Answers

2005

1. The condition on R, L and C such that the step response y(t) in figure has no oscillations, is

Solution: https://www.youtube.com/watch?v=JfYzFU9Oc-0

2. 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

3. In a series RLC circuit, R = 2 kΩ, L = 1 H, and C = 1/400 µF. The resonant frequency is
a) 2 x 10⁴ Hz
b) (1/π) x 10⁴ Hz
c) 10⁴ Hz
d) 2π x 10⁴ Hz

Solution: https://www.youtube.com/watch?v=B9Uk_uA0JbA

4. 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

5. The first and Last critical frequency of an RC driving point impedance function must respectively be
a) a zero and a pole
b) a zero and a zero
c) a pole and a pole
d) a pole and a zero

Solution: https://www.youtube.com/watch?v=noq2x3cDycY

6. For the circuit in figure, the instantaneous current i₁(t) is

Solution: https://www.youtube.com/watch?v=BcmlFVwT5C4

7. Impedance Z as shown in figure is

a) j29 Ω
b) j9 Ω
c) j19 Ω
d) j39 Ω

Solution: https://www.youtube.com/watch?v=tPOeNM7EELI

8. 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

9. 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

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

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

11. 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

GATE 2006 ECE Network Theory - Complete Video Solutions with Answers

2006

1. 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

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

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

3. The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero respectively. The above property will be satisfied by
a) RL network only
b) RC network only
c) LC network only
d) RC as well as RL networks

Solution: https://www.youtube.com/watch?v=L4AUTybSCjk

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

5. In the figure shown below, assume that all the capacitors are initally 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

6. A negative resistance R_neg is connected to a passive network N having driving point impedance Z₁(s) as shown below. For Z₂(s) to be positive real,

Solution: https://www.youtube.com/watch?v=ESM5mIZBEeU

GATE 2003 ECE Network Theory - Complete Video Solutions with Answers

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. 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

3. 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

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

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

5. 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

6. 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.

Common circuit for Questions 7 & 8:
Assume that the switch S is in position 1 for a long time and thrown to position 2 at t=0.

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

8. 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 (7 & 8): https://www.youtube.com/watch?v=IiAPEkdgqQQ

9. 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

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

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

GATE 2007 ECE Network Theory - Complete Video Solutions with Answers

2007

1. 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

2. 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

3. 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

4. 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

5. 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

6. In the AC network shown in the figure, the phasor voltage V_AB(in volts) is:

Solution: https://www.youtube.com/watch?v=CNz1YebFlDw

GATE 2008 ECE Network Theory - Complete Video Solutions with Answers

2008

1. In the following graph, the number of trees (P) and the number of cut-sets (Q) are

a) P = 2, Q = 2
b) P = 2, Q = 6
c) P = 4, Q = 6
d) P = 4, Q = 10

2. 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

3. The Thevenin equivalent impedance Z_TH between the nodes P and Q in the following circuit is

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

4. 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: 5 & 6
The following series RLC circuit with zero initial conditions is excited by a unit impulse function δ(t).

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

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

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

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

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

GATE 2009 ECE Network Theory - Complete Video Solutions with Answers

2009

1. 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

2. 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

3. 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

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

5. 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

6. 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

GATE 2010 ECE Network Theory - Complete Video Solutions with Answers

2010

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

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

2. 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

3. 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