JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II NETWORK ANALYSIS AND TRANSMISSION LINES Previous Question Paper (March - 2021 - R18)

A cutset is a minimal set of branches in a connected graph such that removing these branches disconnects the graph into exactly two separate components. A basic cutset is a cutset that contains exactly one tree branch and any number of links (chords).

To obtain the basic cutset matrix (Q_f):

1. Select a spanning tree of the graph.
2. For each tree branch, define a cutset by removing that branch and identifying the links that must also be removed to partition the graph into two parts.
3. Assign a reference direction to the cutset, typically matching the direction of the tree branch.
4. Construct the matrix where rows represent the basic cutsets and columns represent all branches of the graph.
5. Fill the entries as follows: +1 if the branch direction aligns with the cutset direction, -1 if it opposes, and 0 if the branch is not in the cutset.

For coupled inductors in series, the total inductance L_eq depends on the orientation of the windings. Given L₁ = L₂ = 5 µH and M = 1 µH:

1. Series Aiding: When the flux produced by both coils adds up, the equivalent inductance is:

2. Series Opposing: When the flux produced by the coils opposes each other, the equivalent inductance is:

The resulting inductance is 12 µH for series aiding connection and 8 µH for series opposing connection.