AMIETE – ET (OLD SCHEME)

Code: AE08                                                                  Subject: CIRCUIT THEORY & DESIGN

Time: 3 Hours                                                                                                     Max. Marks: 100

NOTE: There are 9 Questions in all.

· Question 1 is compulsory and carries 20 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.

· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.

· Any required data not explicitly given, may be suitably assumed and stated.

Q.1       Choose the correct or the best alternative in the following:                                 (2 10)

a.

In the circuit shown, I is given by   

(A)  –2A.                                           

                   (B)  2A.

(C)   3A.                                            

(D)  4A.

b. A series RLC circuit has R=10,000 ohms, L=10mH, C=1μF. The resonant frequency ω_o(rad/sec) is given by

(A) .                                            (B) .

(C) .                                            (D) .

c. In the circuit shown, steady state is reached

                                                           with S-open. S is closed at t=0 At t= , the voltage across ‘L’ is given by

(A)  0.                                                

(B)  6.

(C)  –6.                                              

(D)  2.

             d.   An instantaneous voltage of  is applied across an element and the instantaneous power is observed to be Then the element is a   

(A)  Resistor.                                     (B)  Inductor.

(C)  Capacitor.                                   (D)  None of the above.

             e.   A system function . The system is at rest for t<0. i(t)=unit step, is given at  t = 0 then v(t) for t > 0 is given by 

(A) . (B)  .

(C)  . (D)  .

             f.    The current i(t), through a 10Ω resistor in series with an inductance, is given by Amperes. The RMS value of the current in the circuit is

                   (A) . (B) .

(C)  5A.                                              (D)  11A.

             g.   Determine the z-parameters of the network

                   shown in Fig.3

(A) 5, 8, 12, 0                                   

(B)  13, 8, 8, 20

(C)  8, 20, 13, 12                               

(D)  5, 8, 8, 12

             h.    The condition AD–BC=1 for a two port network implies that the network is a

(A) reciprocal network.                      (B) lumped element network.

(C) lossless network.                           (D) unilateral element network.

             i.    The value of the resistance ‘R’ in Fig.4 shown is adjusted such that the power dissipated in the 2Ω resistor

                   is maximum. Under this condition

(A) The value of R is zero ohm.          

(B)  The value of R is 4 ohms.

(C) The power dissipated in the

       2 ohms resistor is18W.                

(D) The value of R is 2 ohms.

             j.    The value of R in the Fig.5 is adjusted

                   so that Power developed by the voltage

                   source is zero Watt. The value of R is 

(A) .                                            

(B) .

(C) .                                            

(D)  .

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2     a.   For the network shown in Fig.6, determine the numerical value of the branch current i₁. All the sources in the network are time invariant.    

                                                                                                                                             (8)

             b.   With switch K in a position a, the network shown in Fig.7 attains equilibrium. At time t=0, the switch is moved to position b. Find the voltage across R₂ as a function of time.

(8)

Q.3     a.   In the network shown in the Fig.8, a steady state is reached with the switch K open. At t=0, the switch is closed.

For the element values given,

                   determine the value of V_a(0–) and

                   V_a(0+).                                                                                                                (8)

             b.   Use the Thevenin equivalent of the network shown in Fig.9 to find the value of R which will receive maximum power.  Find also this power.                                                      (8)

Q.4     a.   Given the ABCD parameters of two port network determine its ‘Z’ parameter.                   (8)

b.   Find the y-parameters of the circuit shown in Fig.10.                                           (8)

Q.5     a.   State the Hurwitz criteria for stability. Determine whether the given polynomial is Hurwitz or not?                                            (8)

             b.   Explain the following:

                   (i) phasor                                             (ii) Resonance

                   (iii) Q                                                  (iv) Damping coefficient                          (8)

  Q.6     a. For the shunt peaking circuit shown in Fig.11 that the admittance Y(s) is of the form  express s₁, s₂ and s₃ in terms of R, L and C.                                                                                                                                                                                                                                                                                                       (8)                                                                                                                                                                                                                                                                                

                                                                                                                                             (8)                                                                                                                                                            (8)

b.   Determine the amplitude and phase for F(J1) from the pole-zero plot in s-plane for the network function (8)

Q.7       a.   Check whether the function is a positive real function.                    (8)

b.   Using Kirchhoff’s laws to the network shown in Fig.12, determine the values of  and .  Verify that the network satisfies Tellegen’s theorem.                     

Q.8       a.   Find the networks for the following function in I Foster and I Caver form .                                                               (8)

b.   Synthesize the voltage ratio as a constant resistance bridged-T network terminated in a 1Ω resistor.                                         (8)

Q.9     a.   The input impedance for the network shown in Fig.13 is .

If Z_o is an LC network:

(i) find the expression for Z_o.

(ii) synthesize Z_o in a Foster series form.                                                             (8)

             b.   Synthesize the 3^rd order low pass Butterworth filter terminated in a 1Ω load resistance.                   (8)