JNTU B.Tech II NETWORK ANALYSIS Previous Question Paper (March - 2021 - R16)

A basic cutset is a minimal set of edges in a graph such that removing these edges disconnects the graph into exactly two components, and at least one of these edges must be a tree branch. The basic cutset matrix (Q) is a matrix that relates the basic cutsets to the branches of the graph. For a graph with 'n' nodes, there are (n-1) tree branches, and each tree branch defines exactly one basic cutset.

The matrix is constructed by identifying the basic cutsets formed by each tree branch. If the graph has 'b' branches and 'n' nodes, the matrix size is (n-1) x b. Each row corresponds to a basic cutset, and each column corresponds to a branch. The entry q_ij is +1 if branch j is in cutset i and oriented in the same direction, -1 if oriented oppositely, and 0 if not present.

Example: Consider a simple graph with 3 nodes (A, B, C) and 3 branches (1, 2, 3) forming a triangle. If branches 1 and 2 are selected as the tree, the basic cutsets are: Cutset 1 (formed by tree branch 1) contains branch 1 and branch 3; Cutset 2 (formed by tree branch 2) contains branch 2 and branch 3. The resulting matrix Q would be a 2x3 matrix mapping these relationships.

Magnetically coupled circuits can be represented by an equivalent T-network to simplify circuit analysis by eliminating the mutual inductance. For two coils with self-inductances L1 and L2 and mutual inductance M, the T-equivalent model consists of three inductors arranged in a T-shape.

The values of the inductors in the T-network are:

In this configuration, the series arm connected to the input is (L1 - M), the series arm connected to the output is (L2 - M), and the common shunt arm is M. This model is valid provided that the mutual inductance M is less than or equal to the smaller of the two self-inductances (M ≤ min(L1, L2)). If the coils are connected in a way that the magnetic flux opposes, the sign of M in the equivalent model is reversed, resulting in (L1 + M), (L2 + M), and -M.