# QUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34)

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1 QUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34) NOTE: FOR NUMERICAL PROBLEMS FOR ALL UNITS EXCEPT UNIT 5 REFER THE E-BOOK ENGINEERING CIRCUIT ANALYSIS, 7 th EDITION HAYT AND KIMMERLY. PAGE NUMBERS OF THE PDF E-BOOK TO BE REFERRED IS ALSO SPECIFIED. UNIT 1 (BASIC CONCEPTS) PART A 1. What is electric current? What is an electric circuit? What are the different types of circuit elements? 2. What are dependent and independent sources? 3. What is (i) Electric Potential; (ii) Potential Difference; (iii) EMF of a source? 4. What is Resistance? Derive the expression for (i) a number of resistors connected in series; (ii) a number of resistors connected in parallel; (iii) The current in a branch when a number of resistors are connected in parallel; 5 (a) What is self inductance? Derive the expression for energy stored in an inductor? 5 (b) What is capacitance? Derive the expression for energy stored in a capacitance? 6. With appropriate illustrations define Kirchhoff s (i) Current Law; (ii) Voltage Law; 7. Explain the procedure used to solve electrical circuits using Kirchhoff s laws. 8. What are linear networks? 1

2 9. Differentiate between (i) Ideal and Practical Voltage sources; (ii) Ideal and Practical Current sources; (iii) Independent and Dependent sources; 10. Explain source transformation and how can it be used to convert (i) a practical voltage source into a practical current source; (ii) a practical current source into a practical voltage source; 11. Explain how the network elements are connected in (i) Delta form; (ii) Star form; 12. Derive the equations to convert (i) Delta network to Star network; (ii) Star network to a Delta network; 13. Define the terms (i) Electric Network; (ii) Passive Network; (iii) Active Network; (iv) Planar and Non-Planar network; (v) Circuit; (vi) Node; (vii) Branch; (viii) Loop; (ix) Mesh; 14. With an example for a general electric circuit explain the procedure for solving it using mesh analysis. 15. With an example explain the procedure to solve a electric circuit using super mesh analysis. 16. With an example explain the procedure for solving an electric circuit using nodal analysis. 17. With an example explain the procedure to solve a electric circuit using super nodal analysis. 18. Give the changes to be incorporated for solving the ac networks using (i) mesh analysis; (ii) super mesh analysis; (iii) nodal analysis; (iv) super nodal analysis; a) For problems on fundamental concepts of charge, current, voltage refer page nos b) For problems on KCL, KVL refer page nos c) For problems on DC analysis using Mesh, Node, Super Mesh, Super Node refer page nos d) For problems on AC Power Analysis refer page nos

3 UNIT 2 (NETWORK TOPOLOGY) 1. What is network topology? 2. Define the terms (i) Path; (ii) Graph of a network; (iii) Oriented or Directed graph; (iv) Degree of a node; (v) Connected graph; (vi) Sub graph; (vii) Proper Sub graph; (viii) Spanning Sub graph; (ix) Tree and Co-Tree; (x) Twig; (xi) Link or Chord; 3. What are the network variables to be solved for a given electric circuit or a network? 4. What is an All Incidence matrix and Reduced Incidence matrix What are their usual notations? 5. For a given oriented network graph, what is the expression for the total number of possible trees? 6. What is Branch Admittance Matrix and Node Admittance Matrix and what are their usual notations? 7. What is Cut Set and Fundamental Cut Set? Explain what is cut-set schedule or the cut-set matrix. Explain the procedure to solve a circuit by using KCL and cut-set matrix. Hence derive the equilibrium equations with tree branch voltages as variables. 8. What is Tie Set? Explain what is Tie-Set schedule or the tie-set matrix. Explain the procedure to solve a circuit by using KCL and tieset matrix. Hence derive the equilibrium equations with loop currents as variables. 9. What is Branch Impedance Matrix and what is its usual notation? What is Loop Impedance Matrix, what its usual notation is and what is the expression for loop impedance matrix in terms of branch impedance matrix. 10. For the oriented graph shown select a tree and write a cut-set schedule. Obtain there from the equations giving the branch voltages in terms of tree branch voltages. 3

4 11. For the network shown, draw the graph, give the incidence matrix, fundamental loop matrix, tie-set matrix. UNIT 3 (NETWORK THEOREMS I) & UNIT 4 (NETWORK THEOREMS II) 1. What is the necessity of using network theorems when Ohm s Law and Kirchhoff s Laws can be used to solve any given electric network? 2. State and explain the Superposition theorem for DC (or AC) circuits with independent (and / or dependent sources) sources. 3. State and explain with proof Millman s theorem. 4. State and explain Reciprocity Theorem. 5. State and explain the procedure for solving network using Thevinin s Theorem. 6. State and explain the procedure for solving network using Norton s Theorem. 7. State and prove the Maximum Power Transfer Theorem for the following cases: (a) The load resistance is equal to the source resistance; (b) The load resistance is equal to the magnitude of source impedance; (c) The load impedance is the complex conjugate of the source impedance; a) For problems on Network Theorems (DC Analysis) refer page nos b) For problems on AC analysis using Mesh, Node, Super Mesh, Super Node, source transformations, star delta conversion, Practical Sources, Network Theorems, refer page nos

5 PART B UNIT 5 (RESONANT CIRCUITS) 1. Explain the phenomenon of resonance. In general what are the electric components present in a resonant circuit? Which are the two types of resonant circuits? 2. Explain the series resonant circuit. Derive the expression for the Quality Factor of a series resonant circuit. 3. Give the frequency response curve of a series resonant circuit. What is the power delivered at resonance and at half-power frequencies? 4. With a neat figure, explain the variation of resistances with frequency. 5. With neat figures, explain (i) the effect of variation of R on frequency response curve; (ii) the effect of variation in the ratio of (L/C) on frequency response curve; 6. For a series resonant circuit, derive the expressions for the halfpower frequencies (f1 and f2). 7. Explain how to achieve series resonance with appropriate figures (i) by varying inductance; (ii) by varying capacitance; 8. With neat figure, explain the variation of voltage across resistance, inductance, and capacitance w.r.t. frequency. 9. Define Frequency Deviation (δ) of a series R-L-C circuit. Derive the expression for the impedance of a series R-L-C circuit in terms of frequency deviation. 10. Derive the expressions for the frequency at which (i) maximum voltage occurs across the capacitor; (ii) maximum voltage occurs across the inductance; 11. Explain the construction of a practical parallel resonant circuit. Derive the expression for the resonant frequency of a parallel resonant circuit. 12. Explain a parallel resonant circuit considering inductance and capacitance to have some resistance. Show that, at resonance the admittance is purely conductive. What is the expression for the current 5

6 at parallel resonance? Give the frequency response curve for a parallel resonant circuit. 13. Derive the expression for a general parallel resonant circuit (R in parallel with L in parallel with C). 14. Explain with figure, the variation of susceptances with frequency. 15. Define and hence, give the expression for the Q-factor of a practical parallel resonant circuit. Give the expression for the bandwidth of the parallel resonant circuit. a) For problems on parallel and series resonance refer page nos UNIT 6 (TRANSIENT BEHAVIOR AND INITIAL CONDITIONS) 1. What kind of equations are to be written and solved for any electrical network consisting of voltage sources, current sources, resistances, inductances, and capacitances? 2. What are initial conditions and final conditions of an electric network? How will be the knowledge of initial conditions useful? 3. Explain the condition or initial conditions (values of currents and voltages) of the circuit elements at t = 0 (before switching), and finding these values at t = 0 + (after switching). 4. Explain the general procedure for finding the initial conditions of the electric network. 5. What are final conditions for the elements in an electric network. 6. What are first order circuits? 7. What is the expression for voltage v(t) for a source free RC circuit? 8. What is the expression for voltage v(t) for a source free RL circuit? 9. What are singularity functions? Give examples. 10. What are transient and steady state responses? 6

7 11. Find the step response of (a) RC circuit; (b) RL circuit; 12. What are second order circuits? 13. Find the response of source free series RLC circuit for the following cases (i) overdamped; (ii) critically damped; (iii) under damped; 14. Find the response of source free parallel RLC circuit for the following cases (i) overdamped; (ii) critically damped; (iii) under damped; 15. Find the step response (by applying of a constant voltage source at the close of a switch) of a series RLC circuit. 16. Find the step response (by applying of a constant current source at the close of a switch) of a parallel RLC circuit. a) For problems on basic RL and RC circuits refer page nos b) For problems on basic RLC circuits refer page nos UNIT 7 (LAPLACE TRANSFORMATION AND APPLICATIONS) 1. What is Laplace Transform? Give the equation for finding the Laplace Transform of function of time f(t). What is one-sided Laplace Transform? Give the complex inversion integral to find the inverse Laplace Transform. 2. What is the major application of Laplace Transform in network analysis? 3. How is the Laplace Transform method of solving differential equations is more advantageous w.r.t. other classical methods? 4. Find the Laplace Transforms of the following standard functions (i) at f(t) = u(t); (ii) f(t) = e and e at ; (iii) f(t) = sinωt and cosωt; (iv) f(t) = n t ; (v) f(t) = sinhωt and coshωt; (vi) Derivative of f(t); (vii) Integral of f(t); (viii) f(t) = δ(t) and δ(t-a) ; (ix) f(t) a periodic function; 5. What is the procedure to use Laplace Transform for solving the given electric network incorporating the initial conditions? 7

8 6. Explain and prove the convolution theorem for two functions of time f 1(t) and f 2 (t). 7. State and prove initial value theorem and final value theorem for a time function f(t). 8. Give the Laplace transformed networks incorporating initial conditions for simple electric network containing (i) ac source and a resistor; (ii) ac source and an inductor; (iii) ac source and a capacitance; a) For problems on LT of time functions, solution of networks, convolution refer page nos UNIT 8 (TWO PORT NETWORK PARAMETERS) 1. What is a 2-port network? Give examples. 2. What are 2-port parameters? How are these parameters helpful in describing a 2-port network? 3. Name the 6 different two-port parameters for a given two-port network. 4. Give the defining equations for (i) y-parameters; (ii) z-parameters; (iii) T-parameters; (iv) T -parameters; (v) h-parameters; (vi) g- parameters; 5. Give the relation between (a) y parameters and other types of parameters; (b) z parameters and other types of parameters; (c) T parameters and other types of parameters; (d) h parameters and other types of parameters; (e) T parameters and other types of parameters; (f) g parameters and other types of parameters; 6. Explain the cascade connection of two port networks. Which type of 2-port parameters is ideal for such a cascade connection? 7. Explain the series connection of two port networks. Which type of 2-port parameters is ideal for such a series connection? 8. Explain the parallel connection of two port networks. Which type of 2-port parameters is ideal for such a parallel connection? 8

9 9. Find the z-parameters for the T representation of a 2-port network. 10. Find the y-parameters for the representation of a 2-port network. 11. When do we say that, an electric network is reciprocal? What are the conditions for an electric network to be reciprocal in terms of (i) y- parameters; (ii) z-parameters; (iii) T-parameters; (iv) T -parameters; (v) h-parameters; (vi) g-parameters; 12. When do we say that, an electric network is symmetrical? What are the conditions for an electrical network to be symmetrical in terms of (i) y-parameters; (ii) z-parameters; (iii) T-parameters; (iv) T - parameters; (v) h-parameters; (vi) g-parameters; a) For problems on two port parameters refer page nos

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