### Network Topology and Mutual Inductance - Topicwise GATE Questions on Network Theory (from 2003)

2003
1. The current flowing through the resistance R in the circuit shown has the form Pcos4t, where p is

a) (0.18 + j0.72)
b) (0.46 + j1.90)
c) - (0.18 + j1.90)
d) - (0.192 + j0.144)

Answer: Data is insufficient as inductor values are not given in the figure.

2004
2. Consider the network graph shown in figure. Which one of the following is NOT a ‘tree’ of this group?

3. The equivalent inductance measured between the terminals 1 and 2 for the circuit shown in figure, is

a) L1 + L2 + M
b) L1 + L2 - M
c) L1 + L2 + 2M
d) L1 + L2 - 2M

2005
4. Impedance Z as shown in figure is

a) j29 Ω
b) j9 Ω
c) j19 Ω
d) j39 Ω

2008
5. 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

2013
6. 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

2014
7. In the magnetically coupled circuit shown in the figure, 56% of the total flux emanating from one coil links the other coil.

The value of the mutual inductance (in H) is _________________