EC-305 Network Analysis - Jun 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
   aIn the circuit of fig-1 at time $t_0$, after the switch S was closed, it is found that $v_2 = +5V$. Determine the value of $i_2(t_0)$ and $\dfrac{di_2(t_0)}{dt}$.

   How to answer

   • Apply KCL at output node: v2 across 2 ohm and 1 ohm + L branch
   • Use v_L = L di2/dt = v2 - 1*i2
   • At t0 with v2=5V find i1(t0)=v2/2 and i(t0) from KCL/KVL with 10V source
   • Solve for i2(t0)=i(t0)-i1(t0)
   • Compute di2(t0)/dt = (v2 - i2)/L
2. 7 Marks
   bIn the circuit of fig-2, the switch S is open and the circuit reaches a steady state. At $t = 0$ the S is closed. Find the current in the inductor for $t > 0$.

   How to answer

   • Find steady state inductor current at t=0- with S open (inductor short)
   • Use continuity iL(0+)=iL(0-)
   • Draw circuit for t>0 with S closed and find Thevenin equivalent seen by inductor
   • Form first-order RL equation iL(t)=i(inf)+(i(0)-i(inf))e^{-Rt/L}
   • Compute time constant and final value
3. 7 Marks
   aIn the circuit of fig-3, switch S is in position 1 for a long time and moved to position 2 at $t = 0$. Find the voltage across the capacitor $v_c(t)$ for $t > 0$.

   How to answer

   • Find vc(0-) = capacitor voltage with S at position 1 steady state
   • Capacitor open and inductor short for DC steady state at 0-
   • Initial inductor current and capacitor voltage continuity at 0+
   • For t>0 series RLC with source disconnected: form second-order equation
   • Solve vc(t) with damping (over/under/critical) using initial conditions
4. 7 Marks
   bState and prove RLC parallel resonance.
   How to answer

   • Define parallel RLC with admittance Y = G + j(wC-1/wL)
   • Derive resonance condition Im(Y)=0 giving w0=1/sqrt(LC)
   • Prove voltage maximum, current minimum, unity power factor at resonance
   • Give Q-factor, bandwidth and phasor diagram
5. 14 Marks
   For the network shown in fig-4 write the tie set matrix for the twigs (2, 4, 5) and determine the loop currents and branch currents for the same.

   How to answer

   • Label branches 1 to 6 and identify tree and twigs (2,4,5)
   • Write tie-set (fundamental loop) matrix B for twigs
   • Form branch impedance matrix and loop equation [Vloop]=[B Z B^T][Iloop]
   • Solve for loop currents then branch currents Ibranch = B^T Iloop
6. 7 Marks
   aBy super position theorem calculate current I in the circuit shown in fig-5

   How to answer

   • State superposition theorem for circuits with independent sources
   • Consider 70V alone (short 50V, open dependent?) and find I1'
   • Consider 50V alone and find I1''; handle dependent source 2I1 retained in each case
   • Sum contributions I1 = I1' + I1'' and solve algebraic equation
7. 7 Marks
   bFind the norton equivalent circuit across terminal AB of the circuit shown in fig-6.

   How to answer

   • Find short-circuit current Isc at AB (Norton current)
   • Find equivalent resistance: deactivate independent source, apply test source due to dependent source
   • Compute IN = Isc and RN = Vth/Isc
   • Draw Norton equivalent with IN in parallel with RN across AB
8. 7 Marks
   aIn the circuit of fig-7 at $t = 0$ the switch is closed Determine the voltage across the capacitor by applying Laplace transform. Assume the initial voltage across the capacitor as 2V. Also draw the S-domain representation of the circuit.

   How to answer

   • Draw S-domain circuit: 10/s current source, R=0.5 ohm, C as 1/sC in series with 2/s initial voltage
   • Write nodal equation in S-domain for Vc(s)
   • Take inverse Laplace to get vc(t) for t>0
   • Show S-domain representation diagram
9. 7 Marks
   bIn circuit of fig-8 the pulse shown is applied as $v(t)$ determine $i(t)$.

   How to answer

   • Express pulse v(t)=u(t)-u(t-1) in time and S-domain
   • Form RL circuit equation V(s)=(R+sL)I(s)
   • Find I(s)=V(s)/(R+sL) with zero initial current
   • Inverse Laplace to get i(t) for 0<t<1 and t>1 (exponential rise and decay)
10. 7 Marks
    aState and prove maximum power transfer theorem.
    How to answer

    • State theorem: max power when ZL = Zth* (or RL=Rth for resistive)
    • Derive by dP/dRL=0 using Thevenin equivalent
    • Prove condition and expression Pmax = Vth^2/4Rth
    • Mention applications
11. 7 Marks
    bFor the circuit shown in fig-9, find the current in the load impedance, $Z_L = (2 + j4)\Omega$ using Millman's theorem.

    How to answer

    • State Millman's theorem for parallel voltage/current sources
    • Convert branches to admittances Y=1/Z
    • Compute Millman voltage Vm = sum(Yk Vk + Ik)/sum(Yk)
    • Find load current IL = Vm/(ZL + equivalent?) or Vm/ZL as per parallel connection
12. 14 Marks
    Obtain the Z and Y parameters of the network shown in fig-10

    How to answer

    • Write open-circuit Z-parameter definitions V1=Z11 I1+Z12 I2
    • Apply I2=0 and I1=0 tests to network with 2,4 ohm and dependent 6I1 source
    • Solve for Z11,Z21 and Z12,Z22
    • Invert Z matrix to get Y-parameters, discuss non-reciprocity
13. 14 Marks
    Write short notes on any two of the following.

    1. a)Tellegen's theorem
    2. b)ABCD parameters
    3. c)Initial and final value theorem
    How to answer

    • Tellegen's theorem: statement, proof via KCL/KVL sum v*b=0
    • ABCD parameters: definition, transmission equations, properties
    • Initial and final value theorems of Laplace: statements and proof sketch
    • Give example/formula for each