GATE 2013 ECE Network Theory - Complete Video Solutions with Answers

2013

1. 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

Answer: B

Solution:   https://www.youtube.com/watch?v=DZotuMVh2vQ

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

Answer: D

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

3. A source V_s(t) = V cos100πt has an internal impedance of (4 + j3) Ω. If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in Ω should be

a) 3

b) 4

c) 5

d) 7

Answer: C

Solution:   https://www.youtube.com/watch?v=_a3PEIDOI08

4. In the circuit shown below, if the source voltage V_s = 100∟53.13^o volts then the thevenin's equivalent voltage in volts as seen by the load resistance R_L is

Answer: C

Solution:  https://www.youtube.com/watch?v=XnD2y6tMyFM

5. The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage V_WX1 = 100 volts is applied across WX to get an open circuit voltage V_YZ1 across YZ. Next, an ac voltage V_YZ2 = 100 volts is applied across YZ to get an open circuit voltage V_WX2 across WX. Then V_YZ1/V_WX1, V_WX2/V_YZ2 are respectively

Answer: B

Solution:  https://www.youtube.com/watch?v=IJX4fwiz-Fo

6. Two magnetically uncoupled inductive coils have Q factors q₁ and q₂ at the chosen operating frequency. Their respective resistances are R₁ and R₂. When connected in series, their effective Q factor at the same operating frequency is

a) q₁ + q₂

b) (1/q₁) + (1/q₂)

c) (q₁R₁ + q₂R₂) / (R₁ + R₂)

d) (q₁R₂ + q₂R₁) / (R₁ + R₂)

Answer: C

Solution:   https://www.youtube.com/watch?v=v7q3ssCyLqw

7. 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

Answer: C

Solution:   https://www.youtube.com/watch?v=9bRJQhA6s3A

Common Data for Questions 8 and 9:

consider the figure shown below

8. The current I_S in Amps in the voltage source, and the voltage V_S in volts across the current source respectively are

a) 13, - 20

b) 8, - 10

c) - 8, 20

d) - 13, 20

Answer: D

9. The current in the 1 Ω resistor in Amps is

a) 2

b) 3.33

c) 10

d) 12

Answer: C

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