### 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

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

3. A source Vs(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

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

5. The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage VWX1 = 100 volts is applied across WX to get an open circuit voltage VYZ1 across YZ. Next, an ac voltage VYZ2 = 100 volts is applied across YZ to get an open circuit voltage VWX2 across WX. Then VYZ1/VWX1, VWX2/VYZ2 are respectively

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)

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

Common Data for Questions 8 and 9:
consider the figure shown below

8. 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

9. The current in the 1 Ω resistor in Amps is
a) 2
b) 3.33
c) 10
d) 12