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

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