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EC-305 · Network Analysis/Unsolved PYQ Paper

EC-305 Network Analysis - Dec 2023 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
    aCalculate the current in the $3\Omega$ resistor for the circuit shown -
    A circuit diagram with three meshes. Left loop has a 10V independent voltage source. A 1 ohm resistor is in the top branch connected to a common branch with a downward 5A independent current source, and a 2 ohm resistor in the bottom branch. The top right loop has a 2 ohm resistor on the right and a horizontal 3 ohm resistor sharing with the bottom right loop. The bottom right loop has a 1 ohm resistor on the right. Mesh currents I1, I2, and I3 are indicated clockwise in the three loops.
    How to answer
    • Identify mesh currents $I_1$, $I_2$, and $I_3$ or node voltages.
    • Formulate KVL equations including supermesh constraint due to the 5A current source between meshes.
    • Solve the system of simultaneous linear equations for the mesh currents.
    • Calculate the net current flowing through the $3\Omega$ resistor ($I_2 - I_3$ or appropriate direction).
  2. 7 Marks
    bThree impedances of $(70.7 + j70.7)\text{ Ohm}$, $(120 + j160)\text{ Ohm}$ and $(120 + j90)\text{ Ohm}$ are connected in parallel across a $250\text{ V}$ supply. Determine i) Admittance of the circuit ii) Supply current iii) Circuit power factor
    How to answer
    • Calculate individual admittances: $Y_1 = 1/Z_1$, $Y_2 = 1/Z_2$, $Y_3 = 1/Z_3$.
    • Find total admittance: $Y_T = Y_1 + Y_2 + Y_3 = G + jB$.
    • Calculate supply current: $I = V \times Y_T$.
    • Determine the overall power factor: $\cos \phi = G / |Y_T|$ (lagging).
  3. 7 Marks
    aExplain the mesh analysis and nodal analysis with example.
    How to answer
    • Define Mesh Analysis based on KVL, selection of loop currents, and formulation of loop equations.
    • Provide an illustrative circuit example demonstrating Mesh Analysis.
    • Define Nodal Analysis based on KCL, selection of reference node, and formulation of node equations.
    • Provide an illustrative circuit example demonstrating Nodal Analysis.
  4. 7 Marks
    bWhat is resonance? Explain parallel resonance condition in detail with circuit and equations.
    How to answer
    • Define electrical resonance (unity power factor condition where inductive and capacitive reactances cancel).
    • Draw circuit diagram of practical parallel R-L and C circuit.
    • Write admittance equation $Y = Y_{RL} + Y_C$ and separate real and imaginary parts.
    • Equate imaginary part (susceptance) to zero to derive resonant frequency $\omega_r$.
    • Derive expression for dynamic impedance $Z_{dynamic} = L / (CR)$.
  5. 7 Marks
    aExplain the following with an example: i) Tree and Co-Tree ii) Twigs and Links iii) Incidence matrix
    How to answer
    • Define Tree (subgraph containing all nodes without closed loops) and Co-tree (complement of tree).
    • Define Twigs (branches of a tree) and Links (branches of co-tree).
    • Define Complete and Reduced Incidence Matrix $[A]$ representing node-branch incidence.
    • Provide a sample directed graph to illustrate Tree, Co-tree, Twigs, Links, and write its incidence matrix.
  6. 7 Marks
    bDraw the graph, one tree and its co-tree for the circuit given below-
    Circuit with labeled nodes a, b, c, d, e. Branch between a and d has an independent current source pointing upward with a parallel resistor. Branch between a and b has a resistor. Branch between a and c has an inductor bridging the top. Branch between b and d has a capacitor. Branch between b and c has a resistor connected in series with an independent voltage source (+ on left). Branch between c and e has a parallel combination of a resistor and a capacitor. Nodes d and e are connected at the bottom.
    How to answer
    • Identify nodes (a, b, c, d, e) and branches from the given circuit.
    • Draw the complete directed/undirected network graph replacing all components by line segments.
    • Select a valid tree connecting all 5 nodes without forming any closed loop (containing $N-1 = 4$ branches).
    • Show the corresponding co-tree containing the remaining link branches.
  7. 7 Marks
    aExplain the concept of principle of duality. Also draw the Dual Circuit of Parallel RLC circuit with Current Source.
    How to answer
    • Explain principle of duality in electrical networks (equations have identical mathematical form under dual variable transformation).
    • List dual pairs: current $\leftrightarrow$ voltage, resistance $\leftrightarrow$ conductance, inductance $\leftrightarrow$ capacitance, loop $\leftrightarrow$ node, series $\leftrightarrow$ parallel.
    • Draw the parallel RLC circuit with a current source.
    • Construct and draw the dual circuit: series RLC circuit driven by an independent voltage source.
  8. 7 Marks
    bFind the current through AB in the given circuit using Norton's theorem.
    Circuit with a 30A current source pointing up on the left in parallel with a branch containing a 10 ohm resistor in series with a 4 ohm resistor. Terminals A and B have a 6 ohm resistor connected between them. To the right of terminal A is a 2 ohm series resistor, which feeds into two parallel branches containing a 3 ohm resistor and a 1 ohm resistor, returning to terminal B line.
    How to answer
    • Remove branch AB ($R_L = 6\Omega$) and short-circuit terminals A and B to calculate Norton current $I_N = I_{sc}$.
    • Deactivate all independent sources (open current source) and calculate Norton equivalent resistance $R_N$ seen across A-B.
    • Draw the Norton equivalent circuit with $I_N$ in parallel with $R_N$ and connected to $R_L = 6\Omega$.
    • Compute the load current $I_{AB} = I_N \times \frac{R_N}{R_N + R_L}$.
  9. 7 Marks
    aFind $V_{ab}$ using Superposition theorem.
    Circuit with an independent 4V voltage source in series with a 10 ohm resistor and a dependent voltage source labeled '3 Vab' (with + on right, - on left). Across the output terminals labeled + at top and - at bottom with voltage Vab, there is an independent 2A current source connected pointing upward.
    How to answer
    • Case 1: Activate 4V source and deactivate 2A current source (open-circuit), keeping the dependent source active; solve for $V_{ab}'$.
    • Case 2: Activate 2A current source and deactivate 4V voltage source (short-circuit), keeping the dependent source active; solve for $V_{ab}''$.
    • Apply superposition: $V_{ab} = V_{ab}' + V_{ab}''$.
  10. 7 Marks
    bGive the statement and prove maximum power transfer theorem with an example.
    How to answer
    • State the Maximum Power Transfer Theorem for DC circuits.
    • Set up the Thevenin equivalent circuit with source $V_{Th}$, internal resistance $R_{Th}$, and load $R_L$.
    • Write expression for power $P_L = \left(\frac{V_{Th}}{R_{Th} + R_L}\right)^2 R_L$.
    • Differentiate $P_L$ with respect to $R_L$ and equate to zero to prove $R_L = R_{Th}$.
    • Derive $P_{max} = \frac{V_{Th}^2}{4 R_{Th}}$ and illustrate with a numerical example.
  11. 7 Marks
    aDetermine the voltage $v_c(t)$ shown in figure, given an initial voltage $v_c(0^-) = -2\text{V}$ using Laplace transform method.
    Circuit with an independent voltage source of value 9u(t) V connected to ground on bottom and to a 3 ohm resistor on top. The 3 ohm resistor connects to a 0.5 F capacitor to ground. The voltage across the capacitor is marked as vc(t) with + at top and - at ground.
    How to answer
    • Convert the time-domain circuit into s-domain with capacitor modeled as impedance $1/(sC)$ in series with a voltage source $v(0^-)/s$ (or parallel current source).
    • Substitute values: $V_{in}(s) = 9/s$, $R = 3\Omega$, $C = 0.5\text{ F}$, $v_c(0^-) = -2\text{ V}$.
    • Write node equation for $V_c(s)$ in the s-domain.
    • Perform partial fraction expansion of $V_c(s)$.
    • Take inverse Laplace transform to obtain $v_c(t)$ for $t \ge 0$.
  12. 7 Marks
    bDiscuss about the step response of an RC circuit using Laplace transform.
    How to answer
    • Draw circuit diagram of series RC circuit excited by a step input $v(t) = V_0 u(t)$.
    • Write differential equation: $R \frac{dq}{dt} + \frac{q}{C} = V_0$ or $R C \frac{dv_c}{dt} + v_c = V_0$.
    • Take Laplace transform assuming zero initial conditions: $V_c(s) = \frac{V_0}{s(1 + sRC)}$.
    • Apply partial fractions: $V_c(s) = V_0 \left(\frac{1}{s} - \frac{1}{s + 1/(RC)}\right)$.
    • Take inverse Laplace transform: $v_c(t) = V_0 (1 - e^{-t/RC}) u(t)$ and plot the response curve.
  13. 7 Marks
    aDescribe the Laplace transform of the waveform shown in figure-
    Waveform plot of f(t) versus t. A pulse train of amplitude 1. Pulses of width 1 are shown: one from t = -2 to -1, one from t = 0 to 1, and one from t = 2 to 3, with zero value between pulses.
    How to answer
    • Identify the waveform as a periodic square pulse train for $t \ge 0$ with amplitude 1, pulse width 1, and period $T = 2$.
    • Express the first cycle $f_1(t)$ using unit step functions: $f_1(t) = u(t) - u(t-1)$.
    • Compute the Laplace transform of the first period: $F_1(s) = \frac{1 - e^{-s}}{s}$.
    • Use the periodicity property: $F(s) = \frac{F_1(s)}{1 - e^{-sT}} = \frac{1 - e^{-s}}{s(1 - e^{-2s})} = \frac{1}{s(1 + e^{-s})}$.
  14. 7 Marks
    bFind the transmission parameters of the following two port network:
    Two-port network diagram. At Port 1, input current I1 flows through a 10 ohm series resistor to an internal node. A 20 ohm shunt resistor connects this node to the common bottom terminal. In the series branch towards Port 2, there is a current-controlled voltage source dependent on I1 labeled '3 I1' with diamond shape (+ on left, - on right). Output current I2 enters Port 2.
    How to answer
    • Define transmission parameters: $V_1 = A V_2 - B I_2$, $I_1 = C V_2 - D I_2$.
    • Apply open-circuit condition at port 2 ($I_2 = 0$) to compute $A = \left.\frac{V_1}{V_2}\right|_{I_2=0}$ and $C = \left.\frac{I_1}{V_2}\right|_{I_2=0}$.
    • Apply short-circuit condition at port 2 ($V_2 = 0$) to compute $B = \left.-\frac{V_1}{I_2}\right|_{V_2=0}$ and $D = \left.-\frac{I_1}{I_2}\right|_{V_2=0}$.
    • Present the final ABCD parameter matrix.
  15. 7 Marks
    aExplain Y-parameters in detail. Also determine its conditions for reciprocity and symmetry.
    How to answer
    • Define short-circuit admittance (Y) parameters with equations: $I_1 = Y_{11} V_1 + Y_{12} V_2$, $I_2 = Y_{21} V_1 + Y_{22} V_2$.
    • Draw equivalent circuit model for Y-parameters.
    • Define and derive condition for reciprocity: $Y_{12} = Y_{21}$.
    • Define and derive condition for symmetry: $Y_{11} = Y_{22}$.
  16. 7 Marks
    bObtain the hybrid parameters in terms of Z-parameters.
    How to answer
    • Write the standard Z-parameter equations: $V_1 = z_{11} I_1 + z_{12} I_2$ and $V_2 = z_{21} I_1 + z_{22} I_2$.
    • Write the standard h-parameter equations: $V_1 = h_{11} I_1 + h_{12} V_2$ and $I_2 = h_{21} I_1 + h_{22} V_2$.
    • Rearrange second Z-equation to express $I_2$ in terms of $I_1$ and $V_2$: $I_2 = -\frac{z_{21}}{z_{22}} I_1 + \frac{1}{z_{22}} V_2$.
    • Substitute $I_2$ into the first Z-equation to express $V_1$ in terms of $I_1$ and $V_2$.
    • Compare coefficients to obtain: $h_{11} = \frac{\Delta Z}{z_{22}}$, $h_{12} = \frac{z_{12}}{z_{22}}$, $h_{21} = -\frac{z_{21}}{z_{22}}$, and $h_{22} = \frac{1}{z_{22}}$.
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