Sunday, May 1, 2016

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

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 :

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 :

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 :

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 :

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 :

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 :

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 :

9. If VA - VB = 6 volts, then VC - VD is

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

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 :

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 :

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

12. The current IS in Amps in the voltage source, and the voltage VS 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):

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 :

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 :

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

Solution :

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

Solution :

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 :

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

Solution :

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

The value of Re/R is ________________
Solution :

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

Solution :

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 :

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

Solution :

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