### GATE 2014 ECE Network Theory - Complete Video Solutions with Answers

2014

1. 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*

2. Consider the configuration shown in the figure, which is a portion of a larger electrical network. For R = 1 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

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

4. 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

5. A periodic variable x is shown in the figure as a function of time.
The root-mean-square (rms) value of x is _________________

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

7. 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

8. 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 kresistor at t = 0+ is ____________

9. 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 1respectively, then the opeating angular frequency (in rad/sec) is ____________________

10. In the h – parameter model of 2 – port network given in the figure shown,
the value of h22 (in siemens) is _____________

11. 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 ?

12. In the magnetically coupled circuit shown in the figure, 56% of the total flus emanating from one coil links the other coil.
The value of the mutual inductance (in H) is _________________

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

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

15. 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

16. In the circuit shown in the figure, the value of node voltage V2 (in volts) is

a) 22 + j 2
b) 2 + j 22
c) 22 – j 2
d) 2 – j 22

17. 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 _____________

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

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

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

21. The steady state output of the circuit shown in the figure is given by y(t) = A(ω) sin(ωt + φ(ω)).
If the amplitude |A(ω)| = 0.25, then the frequency ω is

22. In the circuit shown in the figure,
the value of Vo(t) (in volts) for t → ∞ is ___________

23. The equivalent resistance in the infinite ladder network shown in the figure is Re.
The value of Re/R is ________________

24. For the two – port network shown in the figure, the impedance (Z) matrix (in ) is

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