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 best alternative in the following:                                         (2x10)

a. Power in  resistor is 20W.  The resistance R is   

(A) .                                          

                   (B) .

(C) .                                         

(D)  .

b.

The Thevenin’s equivalent circuit to the left of AB in Fig.2 has given by

(A) (B)

(C)  1 (D)

c. The energy stored in a capacitor is 

(B) (B)

(C) (D)

             d.   The Fig.3 shown are equivalent of each other then  

(A) (B)

(C) (D)

             e.   For the circuit shown in Fig.4, the voltage across

                   the last resistor is V.  All resistors are of . 

                   The  is given by

(A) 13V.                                            (B)  8V.

(C)  4V.                                              (D) 1V.                         

             f.    In the circuit shown in  Fig.5, the switch  s

                   is closed at t = 0 then the steady state value

                   of the current is

                   (A)  1 Amp.                                        (B)  2 Amp.

(C)  3 Amp.                                        (D)  Amp.

             g.   The z parameters of the network shown in Fig.6 is

(A) (B)

(C) (D) 

             h.    For the pure reactive network the following condition to be satisfied

(A)

(B)

(C)

(D)

                   Where  &  even part of the numerator and denominator and  are odd parts of the numerator & denominator of the network function.

             i.    The network has a network function .  It is

(A) not a positive real function.            (B)  RL network.

(C) RC network.                                 (D)  LC network.

             j.    The Q factor for an inductor L in series with a resistance R is given by 

(A) (B)

(C) (D) 

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2     a.   For the circuit shown in Fig.7.  Determine the current  and .                    (8)

             b.   In the network of the  Fig.8,  the switch K is  open and network reaches a steady state.  At t = 0, switch K is closed.  Find the current in the inductor for t > 0.                                                                (8)

Q.3     a.   The network shown in the accompanying Fig.9 is in the steady state with the switch K closed.  At t = 0 the switch is opened.  Determine the voltage across the switch  and  at .           (6)

             b.   Define Thevenin’s theorem.                                                                               (4)

c.   It is required to find the current  in the resistor , by using Thevenin's theorem: The network shown in Fig.10 is in zero state until       t = 0 when the switch is closed.                                            (6)

Q.4     a.   For the given network in Fig.11, determine the value of  that will cause the power in  to have a maximum value.  What will be the value of power under this condition.                                 (8)

b.   In the network shown in Fig.12         and and the

                   network is operating in the steady state – For the element values as given, determine the node to datum voltage .                                     (8)

Q.5     a.   Determine the amplitude and phase for F(J4) from the pole zero plot in      s-plane for the network function .                         (8)

             b.   A network function consists of two poles at  as given in the Fig.13.  Show that the square of the amplitude response  is maximum at . (8)

Q.6   a. Following short circuit currents and voltages are obtained experimentally for a two port network

(i) with output short circuited

(ii) with input short circuited

                   Determine Y-parameters.                                                                                   (8)

b.   The network of the Fig.14 contains a current controlled current source.  For the network find the z-parameters.                                                                                                        (8)

  Q.7     a.   In the network of Fig.15, K is changed from position a to b at t = 0.  Solve for i, , and  at t = 0 + if R = , L=1H, C=0.1 , and     V = 100 V.                                                    (8)

b.   Given  what are the restrictions on ‘X’.  For z(s) to be a positive real function and find ‘X’ for  to have second order zero at .                                                     (8)

Q.8     a.   List out the properties of LC immittance function and then realize the network having the driving point impedance function  by continued fraction method.        (8)

             b.   For the network function  synthesize in one Foster and one Cauer form.                                                                   (8)

Q.9     a.   The voltage ratio transfer function of a constant-resistance bridged-T network is given by  synthesize the network that terminated in a  resistor.                                                      (8)

b.   Find the poles of system functions for low-pass filter with n =3 and n = 4 Butterworth characteristics. (Do not use the tables)                                (8)