Electrical Circuit Analysis - B.Tech 3rd Semester Special Exam., 2020

2020•Semester 2•Civil-CA•End Semester
Bihar Engineering University, Patna
B.Tech 3rd Semester Special Exam., 2020

Electrical Circuit Analysis

Time: 03 HoursCode: 100306 (PCC-EEE-01)Full Marks: 70

Instructions:

  1. The marks are indicated in the right-hand margin.
  2. There are NINE questions in this paper.
  3. Attempt FIVE questions in all.
  4. Question No. 1 is compulsory.
Q.1 Answer any seven questions of the following:[14]

  1. Find the current I in the circuit of Fig. 1 by using the superposition theorem. [DIAGRAM INSTRUCTION: A circuit with a 1A upward current source, a parallel 4 ohm resistor, followed by a T-network (1 ohm, 2 ohm, 3 ohm) and a 1V DC source.]

    Question Diagram

  2. In Fig. 2, find the value of \( R_{Th} \) and \( I_{SC} \).

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  3. Find the value of \( R_{L} \) of Fig. 3 so that the maximum power can be transferred. [DIAGRAM INSTRUCTION: A circuit with two DC sources and an independent 1A current source, mixed with 10 ohm resistors, ending in load resistor RL.]

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  4. Find the Z-parameters of the two-port network shown in Fig. 4.

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  5. Two coupled coils have self-inductances \( L_{1}=50 \text{ mH} \) and \( L_{2}=200 \text{ mH} \) and a coefficient of coupling \( k=0.5 \). If coil 2 has 1000 turns, and \( i_{1}=5.0\sin(400t)\text{A} \), find the voltage at coil 2.

  6. four 2-mark questions are missing

Q.2 Solve all questions :[14]

  1. Use the superposition theorem in the circuit shown in Fig. 7 to find current I. [DIAGRAM INSTRUCTION: A 10V DC source connected to a 5 ohm resistor, a dependent voltage source \( 2V_{x} \), a shunt 2 ohm resistor (with voltage \( V_{x} \)), and a 2A independent current source.]

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  2. Draw the Thévenin's equivalent circuit of Fig. 8 and hence find the current through \( R=2\Omega \). (All the resistances shown in the figure are in ohm).

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  3. State compensation theorem.

Q.3 Solve all questions :[14]

  1. Find the current \( I_{0} \) of Fig. 9 using the superposition theorem.

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  2. In the circuit of Fig. 10, find the effective value of the resistance seen by the source \( V_{s} \).

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  3. Define incidence matrix. Find the complete incidence matrix of the graph shown in Fig. 11.

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Q.4 Solve all questions :[14]

  1. Define the g-parameters of an electrical circuit.

  2. Find the g-parameters in the circuit shown in Fig. 12.

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  3. Find the Z-parameters and Y-parameters of the circuit shown in Fig. 13.

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Q.5 Solve all questions :[14]

  1. Find the Laplace transform of \( f(t)=e^{-\alpha t}\cos(\omega t) \), \( \alpha>0 \).

  2. Calculate the inverse Laplace transform of \( F(s)=\frac{1}{s(s^{2}-a^{2})} \).

  3. In the series R-C circuit, the capacitor has an initial charge 2.5 mC. At \( t=0 \), the switch is closed and a constant-voltage source \( V=100\text{ V} \) is applied. Use the Laplace transform method to find the current in the circuit after closing the switch.

Q.6 Solve all questions :[14]

  1. Draw the graph for the given incidence matrix:
    \( [A] = \begin{bmatrix} -1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & -1 & 0 & 0 & 0 & -1 & 1 \\ 0 & 0 & -1 & 0 & -1 & 0 & -1 \\ 0 & 0 & 0 & 0 & -1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 0 \end{bmatrix} \)

  2. Find the cut-set matrix from the graph as shown in Fig. 14.

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  3. Consider the network shown in Fig. 15, draw the graph and determine (i) number of links, (ii) rank of the graph and (iii) total number of trees.

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Q.7 Solve all questions :[14]

  1. State the characteristics of an ideal transformer.

  2. Define r.m.s. value, form factor, peak factor, complex power and half power frequency.

  3. Calculate the resonant frequency of a series R-L-C circuit.

  4. Obtain the current in each branch of the network shown in Fig. 16, using the mesh current method.

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Q.8 Solve all questions :[14]

  1. Obtain the total power supplied by the 60 V source and the power absorbed in each resistor in the network of Fig. 17.

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  2. Compute the mesh currents of Fig. 18.

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  3. Define supermesh and supernode.

Q.9 Solve all questions :[14]

  1. Derive step response of a series R-C circuit.

  2. Define forced response and natural response.

  3. For the circuit shown in Fig. 19, the switch K is moved from position 1 to position 2 at \( t=0 \text{ s} \). Find the current \( i(t) \) assuming \( i(0_{-})=2\text{ A} \) and \( V_{c}(0_{+})=2\text{ V} \).

    Question Diagram