EX-304 Network Analysis - Jun 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
   aFind the current $i_x$ in the circuit shown below by using nodal analysis.

   

   How to answer

   • Convert to phasor domain at $\omega=4$ rad/s: $j\omega L$, $1/j\omega C$.
   • Write nodal equations at non-reference nodes including supernode/dependent source $2i_x$.
   • Express $i_x$ in terms of node voltage.
   • Solve for phasor $I_x$ and write $i_x(t)$ in time domain.
2. 7 Marks
   bFor the circuit in figure find $V_o$.

   

   How to answer

   • Write mesh equations with mutual term $j\omega M=j1\,\Omega$.
   • Account for dot convention for sign of mutual voltage.
   • Solve primary and secondary mesh currents.
   • Compute $V_o = I_2 \times 1\,\Omega$ magnitude and phase.
3. 7 Marks
   aExplain the following with an example:

   1. i)Tree and Co-Tree
   2. ii)Twigs and Links
   How to answer

   • Define graph, tree with n-1 branches.
   • Define co-tree as remaining links.
   • Give example graph and identify twigs vs links.
   • State number of twigs and links relation.
4. 7 Marks
   bIn the circuit shown in Figure, the switch is initially in position 1 for a long time. Derive the expression for $i(t)$ for $t > 0$ if the switch is transferred to position 2 at $t = 0$.

   

   How to answer

   • Find inductor current at $t=0^-$ with switch at 1 for long time (steady DC).
   • Apply $i_L(0^+)=i_L(0^-)$ for $t>0$ circuit with switch at 2.
   • Form RL first-order equation and time constant $\tau=L/R_{eq}$.
   • Write $i(t)=i(\infty)+[i(0)-i(\infty)]e^{-t/\tau}$ for $t>0$.
5. 7 Marks
   aState and explain the Norton's theorem for A.C excitation with suitable example.
   How to answer

   • State Norton theorem for AC: equivalent current source in parallel with impedance.
   • Explain steps to find $I_N$ and $Z_N$.
   • Give AC example with phasor calculation.
   • Show equivalent circuit.
6. 7 Marks
   bFind the value of R in the circuit shown in figure such that maximum power transfer takes place. What is the amount of this power?

   

   How to answer

   • Find Thevenin equivalent seen from terminals of R.
   • Set $R=R_{Th}$ for maximum power transfer.
   • Compute $P_{max}=V_{Th}^2/4R_{Th}$.
   • State numerical values of R and power.
7. 7 Marks
   aVerify the Tellegen's theorem for the circuit shown.

   

   How to answer

   • Compute branch voltages and currents (80V source, 10,30,4,50 ohm, 10A source).
   • Evaluate $\sum v_k i_k$ for all branches with sign.
   • Show algebraic sum equals zero.
   • Conclude Tellegen's theorem verified.
8. 7 Marks
   bUsing Laplace Transform, solve for the current i(t) in the RLC circuit. The capacitor is initially charged to a voltage of 2V.

   

   How to answer

   • Draw s-domain circuit with initial capacitor voltage 2V.
   • Write KVL equation $I(s)[R+sL+1/sC]=V_{C}(0)/s$ form.
   • Take inverse Laplace to get damped $i(t)$.
   • Substitute R=1, L=0.5H, C=4F values.
9. 7 Marks
   aDetermine the initial and final values of the current where $$I(S) = \frac{0.42}{S(S^2 + 0.35s + 0.816)}$$
   How to answer

   • Apply initial value theorem $i(0^+)=\lim_{s\to\infty}sI(s)$.
   • Apply final value theorem $i(\infty)=\lim_{s\to 0}sI(s)$.
   • Substitute $I(S)=0.42/[S(S^2+0.35s+0.816)]$.
   • Give numerical initial and final currents.
10. 7 Marks
    bR-C series circuit is suddenly excited from a step voltage V. Derive an expression for the current as a function of time and draw the graph current Vs Time
    How to answer

    • Write KVL for step V applied to R-C series with zero initial charge.
    • Solve first-order equation for $q(t)$ and $i(t)=(V/R)e^{-t/RC}$.
    • Explain time constant.
    • Sketch exponentially decaying current vs time starting at V/R.
11. 7 Marks
    aFor the given triangular wave form, determine the Fourier series expansion.

    

    How to answer

    • Describe triangular periodic waveform period T, peak V.
    • Use symmetry to find Fourier coefficients $a_0, a_n, b_n$.
    • Show only cosine terms with $1/n^2$ dependence.
    • Write final series expansion.
12. 7 Marks
    bDetermine the 'h' parameters of the network shown in figure. https://www.rgpvonline.com

    

    How to answer

    • Write port equations $V_1, I_1$ in terms of $V_2, I_2$.
    • Apply $V_2=0$ and $I_1=0$ conditions for h-parameters.
    • Solve with dependent sources $2V_2$ and $2V_1$.
    • Present $h_{11}, h_{12}, h_{21}, h_{22}$.
13. 7 Marks
    aDerive expressions for the Y-parameters in terms of ABCD parameters of a two-port network.
    How to answer

    • Start from ABCD definitions $V_1=AV_2-BI_2$, $I_1=CV_2-DI_2$.
    • Invert to express $I_1, I_2$ in terms of $V_1, V_2$.
    • Identify $Y_{11}, Y_{12}, Y_{21}, Y_{22}$ in terms of A,B,C,D.
    • State determinant $\Delta=AD-BC$ role.
14. 7 Marks
    bA typical two-port network is characterized by the equation $2V_1 + 4 I_2 = I_1$ $V_2 + 6V_1 = 8 I_2$ Determine:

    1. i)$y_{11}$
    2. ii)$z_{12}$
    3. iii)$h_{21}$
    4. iv)C
    How to answer

    • Rewrite given equations in standard y, z, h forms.
    • Compute $y_{11}=I_1/V_1|_{V_2=0}$ etc.
    • Compute $z_{12}$ and $h_{21}$.
    • Compute transmission parameter C.
15. 14 Marks
    Write a short notes on any Two:

    1. i)Cut Set Matrix
    2. ii)Compensation Theorem
    3. iii)Open Circuit Impedance Parameters
    4. iv)Terminated Two Port Network
    How to answer

    • Select any two topics from list.
    • Give definition, statement or matrix where applicable.
    • Explain with example/diagram.
    • State applications.