EC-305 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
   aFind the voltage across the dependent current source

   

   How to answer

   • Identify node a and set its voltage as v
   • Write KCL equation at node a
   • Express controlling current I_1 in terms of nodal voltage v
   • Solve for voltage v across the dependent source
2. 7 Marks
   bDiscuss dot Convention used in Magnetically coupled Circuits with suitable example.
   How to answer

   • Define dot convention rule for magnetically coupled coils
   • Explain sign of mutually induced voltage with respect to current entering or leaving the dot
   • Draw circuit diagram with two coupled inductors having dot markings
   • Provide a suitable mesh equation example
3. 7 Marks
   aAn impedance $Z_1 = 10 + j10\ \Omega$ is connected in parallel with another impedance of resistance $8.5\ \Omega$ and a variable capacitance connected in series. Find $C$ such that the circuit is in resonance at $5\text{ KHz}$
   How to answer

   • Find admittance of branch 1: $Y_1 = \frac{1}{10+j10} = 0.05 - j0.05\text{ S}$
   • Write admittance of branch 2: $Y_2 = \frac{1}{8.5 - jX_C} = \frac{8.5 + jX_C}{(8.5)^2 + X_C^2}$
   • Set total imaginary part (susceptance) to zero: $\frac{X_C}{72.25 + X_C^2} - 0.05 = 0$
   • Solve quadratic equation for $X_C$
   • Calculate $C = \frac{1}{2\pi f X_C}$ for $f = 5000\text{ Hz}$
4. 7 Marks
   bFor the network shown in figure below draw the oriented graph and frame the cut-set matrix

   

   How to answer

   • Label all nodes and branches with arbitrary orientation
   • Draw the oriented graph representing the circuit topology
   • Select a suitable tree of the graph
   • Identify fundamental cut-sets associated with each twig/tree branch
   • Formulate and write the cut-set matrix (fundamental cut-set matrix)
5. 7 Marks
   aExplain the following with suitable example: i) Sub graph ii) Connected graph iii) Planar graph iv) Tree and Co-Tree
   How to answer

   • Define Sub graph with an illustrative figure
   • Define Connected graph (path between every pair of vertices)
   • Define Planar graph (can be drawn on a plane without intersecting edges)
   • Define Tree (connected subgraph containing all nodes without closed loops) and Co-Tree (complementary graph consisting of links)
   • Provide diagrammatic examples for each
6. 7 Marks
   bDraw the parallel resonant circuit and derive the expression for resonant frequency.
   How to answer

   • Draw standard parallel resonant circuit (RL branch in parallel with RC or C branch)
   • Write total admittance expression $Y(j\omega)$
   • Separate real and imaginary components (conductance and susceptance)
   • Apply condition for resonance: Susceptance $B = 0$
   • Solve for $\omega_0$ and $f_0$
7. 7 Marks
   aState and explain Thevenin's theorem with suitable example.
   How to answer

   • State Thevenin's theorem statement accurately
   • Explain calculation of $V_{th}$ (open-circuit voltage) and $R_{th}$ (equivalent resistance looking into the terminals)
   • Draw Thevenin equivalent circuit ($V_{th}$ in series with $R_{th}$ and $R_L$)
   • Demonstrate application with a simple circuit example
8. 7 Marks
   bFind the value of $R_L$ for maximum power transfer in the circuit shown below. And find the maximum power.

   

   How to answer

   • Remove load resistor $R_L$ connected between terminals $a$ and $b$
   • Determine Thevenin resistance $R_{th}$ by deactivating independent sources ($12\text{ V} \rightarrow$ short, $2\text{ A} \rightarrow$ open): $R_{th} = 2 + 3 + (6 \parallel 12) = 5 + 4 = 9\ \Omega$
   • Hence $R_L = R_{th} = 9\ \Omega$
   • Find open-circuit voltage $V_{th}$ across terminals $a-b$ using nodal/mesh analysis
   • Calculate maximum power using $P_{max} = \frac{V_{th}^2}{4 R_{th}}$
9. 7 Marks
   aFor the circuit given below, Find the current 'I' and then verify the reciprocity theorem

   

   How to answer

   • Set up mesh/nodal equations to calculate current $I$ in the $4\ \Omega$ bottom branch
   • Interchange the excitation ($5\text{ V}$ source) to the branch where $I$ was measured
   • Calculate the new current in the original source branch
   • Show that the ratio of excitation to response is equal in both cases, verifying the reciprocity theorem
10. 7 Marks
    bA $200\Omega$ resistor is in series with an inductor L. The initial value of the inductor current is $5\text{ mA}$ and its value after $5\text{ms}$ is $3\text{ mA}$. Find the time constant and the inductance.
    How to answer

    • Write decay current expression: $i(t) = I_0 e^{-t/\tau}$
    • Substitute values: $3 = 5 e^{-5 \times 10^{-3}/\tau} \implies e^{-0.005/\tau} = 0.6$
    • Calculate $\tau$: $\tau = -0.005 / \ln(0.6) = 0.009789\text{ s} \approx 9.79\text{ ms}$
    • Calculate inductance: $L = R \times \tau = 200 \times 0.009789 \approx 1.958\text{ H}$
11. 7 Marks
    aThe network as shown in figure below reaches a steady state with switch K closed. At $t = 0$ switch K is opened. Find the $I(t)$.

    

    How to answer

    • Determine initial inductor current $i(0^-) = i(0^+)$ when switch K is closed in steady state
    • For $t > 0$, switch K is open; identify the single loop circuit
    • Find the final steady-state current $i(\infty)$
    • Determine equivalent resistance $R_{eq}$ and time constant $\tau = \frac{L}{R_{eq}}$
    • Write full transient equation $i(t) = i(\infty) + [i(0^+) - i(\infty)] e^{-t/\tau}$
12. 7 Marks
    bState and explain Initial Value and Final value theorem
    How to answer

    • State Initial Value Theorem: $\lim_{t \to 0} f(t) = \lim_{s \to \infty} s F(s)$
    • State conditions for IVT validity
    • State Final Value Theorem: $\lim_{t \to \infty} f(t) = \lim_{s \to 0} s F(s)$
    • State conditions for FVT validity (poles of $s F(s)$ must lie in the left half of the s-plane)
    • Provide a simple illustrative example
13. 7 Marks
    aDetermine the 'h' parameters of the network shown in figure

    

    How to answer

    • Define h-parameter equations: $V_1 = h_{11} I_1 + h_{12} V_2$ and $I_2 = h_{21} I_1 + h_{22} V_2$
    • Short-circuit port 2 ($V_2 = 0$) to find $h_{11} = \frac{V_1}{I_1}\Big|_{V_2=0}$ and $h_{21} = \frac{I_2}{I_1}\Big|_{V_2=0}$
    • Open-circuit port 1 ($I_1 = 0$) to find $h_{12} = \frac{V_1}{V_2}\Big|_{I_1=0}$ and $h_{22} = \frac{I_2}{V_2}\Big|_{I_1=0}$
    • Formulate and state the resulting h-parameter matrix
14. 7 Marks
    bDefine Z and Y parameters of a Two port network and determine the relationship between the above parameters.
    How to answer

    • Define Z-parameters: $[V] = [Z][I]$ with individual parameter definitions
    • Define Y-parameters: $[I] = [Y][V]$ with individual parameter definitions
    • Express relationship in matrix form: $[Y] = [Z]^{-1}$
    • Determine inverse matrix of $[Z]$ using determinant $\Delta Z = Z_{11}Z_{22} - Z_{12}Z_{21}$
    • Equate corresponding elements: $Y_{11} = \frac{Z_{22}}{\Delta Z}$, $Y_{12} = -\frac{Z_{12}}{\Delta Z}$, $Y_{21} = -\frac{Z_{21}}{\Delta Z}$, $Y_{22} = \frac{Z_{11}}{\Delta Z}$
15. 14 Marks
    Write a short notes on any two: i) Image Parameter ii) Steady State Analysis iii) Controlled and un controlled sources iv) Dual Networks
    How to answer

    • Image Parameters: definition of image impedances $Z_{i1}, Z_{i2}$ and propagation constant $\theta$
    • Steady State Analysis: AC/DC sinusoidal steady-state, phasor domain representations, and impedance techniques
    • Controlled and uncontrolled sources: definitions, VCVS, VCCS, CCVS, CCCS vs independent voltage/current sources with symbols
    • Dual Networks: concept of duality, dual pairs (voltage-current, resistance-conductance, inductance-capacitance, loop-node)