JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II NETWORK ANALYSIS Previous Question Paper (August/September - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
For the network shown in figure 1, write a Tie-set schedule and then find all the branch currents and voltages.
Answer
A tie-set schedule is constructed by selecting a tree of the network and identifying the fundamental loops formed by adding each link (chord) one at a time. For a network with b branches, n nodes, and l = b - n + 1 links, the tie-set matrix B relates branch currents Ib to link currents Il via the relation Ib = BTIl.
To solve for branch currents and voltages:
- Select a tree: Choose a set of branches that connect all nodes without forming a loop. The remaining branches are designated as links.
- Form the Tie-set Matrix: For each link, identify the unique fundamental loop it creates when added to the tree. Assign a direction to the link current and record the orientation of tree branches in the loop (+1 if aligned, -1 if opposite, 0 if not in the loop).
- Apply KVL: Express the loop equations in matrix form: B Zb BT Il = B E, where Zb is the diagonal matrix of branch impedances and E is the vector of branch voltage sources.
- Solve for Link Currents: Calculate Il = (B Zb BT)-1 B E.
- Determine Branch Currents: Use Ib = BT Il to find all branch currents.
- Determine Branch Voltages: Calculate individual branch voltages using Vb = Zb Ib (or Vb = Zb Ib - E if sources are present in branches).
The resulting tie-set schedule provides a systematic basis for analysis, ensuring that Kirchhoff's laws are satisfied while reducing the number of simultaneous equations to the number of fundamental loops.
Define self and mutual inductances and derive the equation for coefficient of coupling.
Answer
Self-inductance (L) is the property of a coil by which it opposes any change in the current flowing through it, defined as the ratio of flux linkage to the current: L = Nφ/I. Mutual inductance (M) is the property by which a change in current in one coil induces an electromotive force in an adjacent coil, defined as M = N₂φ₂₁/I₁.
To derive the coefficient of coupling (k), consider two coils with self-inductances L₁ and L₂. The flux produced by coil 1 is φ₁, and the flux linking coil 2 is φ₂₁ = k₁φ₁. The flux produced by coil 2 is φ₂, and the flux linking coil 1 is φ₁₂ = k₂φ₂. The mutual inductances are M = N₂φ₂₁/I₁ and M = N₁φ₁₂/I₂. Multiplying these gives M² = (N₂k₁φ₁/I₁)(N₁k₂φ₂/I₂). Since L₁ = N₁φ₁/I₁ and L₂ = N₂φ₂/I₂, we get M² = k₁k₂L₁L₂. Defining k = √(k₁k₂), we obtain the relation:
A toroidal core of radius 6 cms is having 1000 turns on it. The radius of cross section of the core 1cm. Find the current required to establish a total magnetic flux of 0.4 mWb. When the core is non magnetic and the core is made of iron having a relative permeability of 4000.
Answer
Sign in to view the complete answer paper.
A coil of R=1KΩ and L=1H is connected to a dc voltage of 100V through a change over switch. At t=0, the switch connects a capacitor of C=0.1μF in series with the coil, excluding the voltage. Solve for I,
Answer
Sign in to view the complete answer paper.
Draw the RL circuit and locus of current vector
Answer
Sign in to view the complete answer paper.
Obtain an expression for resonant frequency of a parallel RLC circuit excited by sinusoidal source.
Answer
Sign in to view the complete answer paper.
State and prove the initial value theorem.
Answer
Sign in to view the complete answer paper.
Using the convolution theorem find f(t) when
Answer
Sign in to view the complete answer paper.
Using Laplace transform determine the current in the circuit shown in the following figure 2 when the switch S is closed at t=0. Assume zero initial condition.
Answer
Sign in to view the complete answer paper.
Find the z and h parameters for the following circuit shown in figure 3.
Answer
Sign in to view the complete answer paper.
Design a constant k low pass filter and write its advantages and disadvantages.
Answer
Sign in to view the complete answer paper.