JNTU
JNTU B.Tech II NETWORK ANALYSIS Previous Question Paper (March - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
For the directed graph shown in figure 1 find the cut set matrix.
Answer
A cut set matrix is a matrix that represents the relationship between the cut sets of a graph and its branches. To determine the cut set matrix for a directed graph, follow these steps:
- Identify all possible fundamental cut sets of the graph. A fundamental cut set is formed by including one tree branch and the necessary links that, when removed, partition the graph into two disjoint sets of nodes.
- Select a spanning tree for the given graph. The number of fundamental cut sets is equal to the number of tree branches, which is (n-1), where n is the number of nodes.
- Define the orientation of each cut set. Typically, the orientation of the cut set is chosen to match the orientation of the tree branch that defines it.
- Construct the matrix where each row represents a fundamental cut set and each column represents a branch of the graph.
- Assign values to the matrix elements:
- +1 if the branch is in the cut set and its orientation matches the cut set orientation.
- -1 if the branch is in the cut set and its orientation is opposite to the cut set orientation.
- 0 if the branch is not included in the cut set.
The resulting matrix, often denoted as Qf, will have dimensions (n-1) × b, where b is the total number of branches in the graph. This matrix is fundamental in network analysis for applying Kirchhoff's Current Law (KCL) to the cut sets of the network.
How to obtain a change in flux in coil? How to find self inductance of a coil?
Answer
A change in magnetic flux through a coil is obtained by varying the magnetic field strength, changing the area of the coil within the magnetic field, or altering the orientation (angle) of the coil relative to the magnetic field lines. Mathematically, flux is defined as Φ = B A cos(θ), so changing any of these three parameters induces a change in flux.
Self-inductance (L) is defined as the ratio of the total flux linkage to the current flowing through the coil, expressed as L = NΦ / I. To find the self-inductance of a coil, one determines the magnetic flux Φ produced by a current I flowing through N turns of the coil. For a solenoid, this is calculated using the formula L = (μ N^2 A) / l, where μ is the permeability of the core material, N is the number of turns, A is the cross-sectional area, and l is the length of the coil.
Explain dot convention of a magnetically coupled coils.
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R=1Ω, L=1H and C=1/2F are connected in series across 2V supply. At t=0+ the switch is in closed position. Find i(t), for t>0.
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Draw the RC circuit and locus of current vector IC with variation of R.
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Derive the equation for Q factor of series RLC circuit.
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State and prove the final value theorem.
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Obtain the Laplace transform of period function shown in figure 2.
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The current function i(t) shown in figure 3 is impressed on a capacitor C. What should be the strength A of the impulse so that the voltage across the C becomes zero for t > 5 secs.
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Find the y and ABCD parameters for the following circuit shown in figure 4.
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Design a constant k high pass filter and write its advantages and disadvantages.
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What are the different types of attenuators? Explain them.
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