EX-304 Network Analysis - Dec 2024 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aDraw the parallel resonant circuit and derive the expression for resonant frequency.
   How to answer

   • Parallel resonant circuit diagram with R-L-C in parallel across source
   • Admittance expression $Y = 1/R + j(\omega C - 1/\omega L)$
   • Resonance condition $Im(Y)=0$ and derivation steps
   • Expression for resonant frequency $f_0 = (1/2\pi)\sqrt{1/LC - R^2/L^2}$ or ideal $1/2\pi\sqrt{LC}$
2. 7 Marks
   bState and explain KCL and KVL with example.
   How to answer

   • Statement of KCL: algebraic sum of currents at node is zero
   • Statement of KVL: algebraic sum of voltages around loop is zero
   • Illustrative example circuit for each
   • Equations for example
3. 7 Marks
   aDefine Graph, oriented graph, Twigs and Cut set matrix.
   How to answer

   • Definition of graph in network topology
   • Definition of oriented/directed graph
   • Definition of twigs with respect to tree
   • Definition of cut-set matrix
4. 7 Marks
   bWhat is incidence matrix? Find the complete incidence matrix for the graph shown in figure.

   

   How to answer

   • Definition of incidence matrix with entries 1, -1, 0
   • Identification of nodes x, y, z and oriented branches 1-5 from figure
   • Construction of rows for nodes vs columns for branches
   • Complete $(3 \times 5)$ incidence matrix
5. 7 Marks
   aFind the voltage drop across $3\Omega$ resistor by superposition theorem.

   

   How to answer

   • Superposition theorem steps: consider one source at a time
   • Voltage contribution due to 10V source alone with 10A open
   • Voltage contribution due to 10A source alone with 10V shorted
   • Algebraic sum to get voltage drop across $3\Omega$
6. 7 Marks
   bState and explain the Norton theorem with example.
   How to answer

   • Statement of Norton theorem: equivalent current source in parallel with resistance
   • Steps to find $I_N$ and $R_N$
   • Illustrative example circuit with calculation
   • Source conversion relation to Thevenin
7. 7 Marks
   aFind the Thevenin equivalent circuit for the following circuit.

   

   How to answer

   • Find open-circuit voltage Vth between A-B
   • Find equivalent resistance Rth seen from A-B
   • Include 5V source effect in Vth and Rth
   • Draw Thevenin equivalent $V_{th}$ in series with $R_{th}$ across A-B
8. 7 Marks
   bState and explain maximum power transfer theorem for DC network.
   How to answer

   • Statement of maximum power transfer theorem for DC
   • Condition $R_L = R_{th}$ for maximum power
   • Derivation $P = I^2 R_L$ and $dP/dR_L=0$
   • Expression for $P_{max} = V_{th}^2/4R_{th}$
9. 7 Marks
   aFind the Fourier series for the given waveform.

   

   How to answer

   • Identify periodic rectangular waveform with amplitude Fm and period T
   • Determine symmetry and Fourier coefficients a0, an, bn
   • Evaluate integrals over 0 to T/2 etc.
   • Write trigonometric Fourier series
10. 7 Marks
    bFind the exponential Fourier series for the given waveform.

    

    How to answer

    • Identify square wave i(t) with amplitude Im vs wt
    • Formula for exponential coefficients $C_n$
    • Evaluation over 0 to 2pi
    • Write series $i(t)=\sum C_n e^{jnwt}$
11. 7 Marks
    aFind the value of $i(0)$ using initial value theorem for the function $I(s) = \frac{2s+3}{(s+1)(s+3)}$
    How to answer

    • Initial value theorem $i(0^+)=\lim_{s\to\infty}sI(s)$
    • Substitute $I(s) = (2s+3)/((s+1)(s+3))$
    • Evaluate limit as $s\to\infty$
    • Result $i(0)=2$
12. 7 Marks
    bWrite the expression and find the Laplace transform for the waveform shown in figure below.

    

    How to answer

    • Time-domain expression $i(t) = (A/T)t$ for $0<t<T$
    • Laplace transform of ramp using $L[t u(t)]$
    • Apply time-shifting / gate function
    • Result $I(s)$ expression
13. 7 Marks
    aObtain the Z parameters for the two port network.

    

    How to answer

    • Z-parameter definitions $V_1=Z_{11}I_1+Z_{12}I_2$, $V_2=Z_{21}I_1+Z_{22}I_2$
    • Open-circuit tests to find $Z_{11}, Z_{22}, Z_{12}=Z_{21}$
    • Simplify 1-2-3-4 ohm network
    • Numerical Z-matrix
14. 7 Marks
    bDefine H parameters of a two port network. Established the relation between H parameters and ABCD parameters.
    How to answer

    • Definitions of H parameters $V_1=h_{11}I_1+h_{12}V_2$, $I_2=h_{21}I_1+h_{22}V_2$
    • Definitions of ABCD parameters
    • Algebraic conversion from one set to other
    • Final relations for A,B,C,D in terms of h
15. 14 Marks
    Write short notes on any two:

    1. i)Controlled sources
    2. ii)Millman's theorem
    3. iii)Y parameters
    How to answer

    • Brief definition and concept of first chosen topic
    • Relevant formula or circuit diagram
    • Key points and application
    • Brief coverage of second chosen topic similarly