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

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

Electrical Circuit Analysis

Time: 03 HoursCode: 100306Full 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 Choose the correct answer of the following (any seven):[14]

  1. The Norton's equivalent of the circuit shown in figure below is

    Question Diagram
    1. \( I_{N}=5/2 \text{ A} \) and \( R_{N}=2\Omega \)
    2. \( I_{N}=4/5 \text{ A} \) and \( R_{N}=1\Omega \)
    3. \( I_{N}=2/5 \text{ A} \) and \( R_{N}=1\Omega \)
    4. \( I_{N}=2/5 \text{ A} \) and \( R_{N}=2\Omega \)

  2. A 10 mH inductor carries a sinusoidal current of 1 A r.m.s. at a frequency of 50 Hz. The average power dissipated by the inductor is

    1. 0 W
    2. 0.25 W
    3. 0.5 W
    4. 1.0 W

  3. Thevenin's equivalent circuit consists of

    1. current source and series impedance
    2. voltage source and series impedance
    3. voltage source and shunt impedance
    4. current source and shunt impedance

  4. A two-element series circuit is connected across an AC source given by \( e=200\sqrt{2}\sin(314t+20) \text{ V} \). The current is found to be \( i=10\sqrt{2}\cos(314t-25) \text{ A} \). Then parameters of the circuit are

    1. \( R=20\Omega \) and \( C=160\mu F \)
    2. \( R=14.14\Omega \) and \( C=225\mu F \)
    3. \( L=45\text{ mH} \) and \( C=225\mu F \)
    4. \( L=45\text{ mH} \) and \( C=160\mu F \)

  5. There are no transients in pure resistance circuits because they

    1. offer high resistance
    2. obey Ohm's law
    3. have no stored energy
    4. are linear circuits

  6. In the below network, the switch K is opened at \( t=0 \). Then \( \frac{dV}{dt} \) at \( t=0^{+} \) is

    Question Diagram
    1. 1000 V/sec
    2. 100 V/sec
    3. 10 V/sec
    4. 1 V/sec

  7. When a number of two-port network is cascaded, then

    1. Z-parameters are added up
    2. Y-parameters are added up
    3. h-parameters are multiplied
    4. ABCD-parameters are multiplied

  8. Two coils are coupled in such a way that the mutual inductance between them is 16 mH. If the inductances of the coils are 20 mH and 80 mH respectively, the coefficient of coupling is

    1. 0.01
    2. 0.4
    3. 0.1
    4. 0.0025

  9. When a unit impulse voltage is applied to an inductor of 1 H, the energy supplied by the source is

    1. 2 J
    2. 1 J
    3. 1/2 J
    4. 1/4 J

  10. The h-parameters \( h_{11} \) and \( h_{22} \) are related to Z and Y-parameters as

    1. \( h_{11}=Z_{11} \) and \( h_{22}=1/Z_{22} \)
    2. \( h_{11}=Z_{11} \) and \( h_{22}=Y_{22} \)
    3. \( h_{11}=1/Y_{11} \) and \( h_{22}=1/Z_{22} \)
    4. \( h_{11}=1/Y_{11} \) and \( h_{22}=Y_{22} \)
Q.2 Solve :[14]

  1. Two mutually coupled identical coils are connected in series having self-inductance \( L=4 \text{ mH} \) and mutual inductance \( M=2 \text{ mH} \).
    What are the maximum and minimum possible values of equivalent inductances?

    Determine the coefficient of coupling between the coils.

Q.3 Solve both questions :[14]

  1. Show that Thevenin's and Norton's theorems are dual to each other.

  2. Using Norton's theorem, find the current in \( 5\Omega \) resistor for the circuit shown below.

    Question Diagram
Q.4 Solve both questions :[14]

  1. When can a two-port circuit be declared as a reciprocal circuit?

  2. Find ABCD parameters for the two-port network shown in the figure below:

    Question Diagram
Q.5 Solve both questions :[14]

  1. Prove that the average power in an AC circuit is given by \( W=VI\cos\phi \), where symbols have their usual meanings.

  2. A voltage of \( e(t)=150\sin(1000t) \) is applied across a series R-L-C circuit, where \( R=40\Omega \), \( L=0.13 \text{ H} \) and \( C=10\mu\text{F} \). (i) Compute the r.m.s. value of the steady-state current. (ii) Find the r.m.s. voltage across the inductor. (iii) Find the r.m.s. voltage across the capacitor. (iv) Determine the active and reactive power supplied by the source.

Q.6 Solve this question :[14]

  1. Determine overall Z-parameters when two 2-port networks with identical \( Z_{11}=Z_{12}=Z_{21}=Z_{22}=2\Omega \) are connected in cascade.

Q.7 Solve this question :[14]

  1. In the R-L-C circuit shown in figure below, \( I_{s}=10 \text{ A} \), \( R=1\Omega \), \( L=1\text{H} \), \( C=1\mu\text{F} \) and \( i_{L}(0^{-})=0 \). Determine the following parameters after the switch is closed at \( t=0 \): (a) \( V(0^{+}) \) (b) \( \frac{dV}{dt} \) at \( t=0^{+} \) (c) \( \frac{d^{2}V}{dt^{2}} \) at \( t=0^{+} \).

    Question Diagram
Q.8 Solve both questions :[14]

  1. An R-L-C tank circuit is composed of components having values as \( R=0.2\Omega \), \( L=100 \text{ mH} \) and \( C=50\mu\text{F} \). Determine the resonance frequency and the corresponding input current at 24 V.

  2. Obtain the values of R, L and C in a series R-L-C circuit that resonates at 1.5 kHz and consumes 50 W from a 50 V a.c. source operating at the resonance frequency. The bandwidth is 0.75 kHz.

Q.9 Solve this question :[14]

  1. For the circuit shown below, obtain the current through the capacitor C at \( t=0^{+} \) using Laplace transform following the switching takes place at \( t=0 \). Assume the capacitor to be initially discharged.

    Question Diagram