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: (2x10)

a.

A voltage source with an internal resistance, supplies power to a load . The power P delivered to the load varies with as

(A) (B)

(C) (D)

b. A series circuit has an impedance , its susceptance is

(A) (B)

(C) (D)

c. If A is the incidence matrix of and B be the loop matrix of network , the condition for the two networks to be duals of each other is that

(A) rank of [A] > rank of [B] (B) rank of [A] < rank of [B]

(C) rank of [A] = rank of [B] (D) None of these

d. In the initially relaxed circuit shown in Fig.1, the switch S is closed at t=0. The value of current at t=0+ will be

(A) zero

(B) -1A

(C) +1A

(D) 100A

e. The closed-loop pole location of

a network is shown in Fig.2.

The nature of the unit step response

would be

(A) (B)

(C) (D)

f. In a given circuit the input voltage and current are given by

The power consumed in the circuit is

(A) 100 watts (B) 50 watts

(C) 25 watts (D) 12.5 watts

g. The voltmeter readings across different circuit elements are as shown in the Fig.3. The reactive component of the current I in the circuit is

(A) 10A (B)5A

(C) zero (D) 2A

h. For the two port network shown in Fig.4, select the correct statement

(A) It does not have z-parameter (B) It has z-parameters

(C) It does not have y-parameters (D) It does not have ABCD parameters

i. A network whose impedance function is is synthesized. It consists of ‘n’ LC tank circuits in series with an inductance and/or a capacitance. The value of ‘n’ is

(A) zero (B) 1

(C) 2 (D) 3

j. The driving-point impedance of an RC network is given by . Its canonical realization will have

(A) 6 elements (B) 5 elements

(C) 4 elements (D) 3 elements

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2 a. State and explain the terminal relationships for ideal R, L and C in reference to network analysis. (6)

b. Define positive real function and write its properties. (10)

Q.3 a. Explain the concepts of duality in reference to electrical networks. Explain the graphical procedure of constructing the dual of a network. (8)

b. Find the voltages across the impedances in circuit shown in Fig.5. Transform the voltage source and impedance to a Norton’s equivalent current source and again find the voltages. Compare results. (8)

Q.4 a. State and illustrate with the help of an example the final value theorem in reference to electric networks. (6)

b. In the network shown in Fig.6, the switch is initially closed for a long time. The switch is opened at t=0. Find differential equation relating and its derivatives with and also evaluate the initial conditions required to solve for . (10)

Q.5 a. State super-position theorem in reference to electrical networks and also give its limitations. (7)

b. Use super-position theorem to find voltage V in the network shown in Fig.7. (9)

Q.6 a. The network shown in Fig.8 has a sinusoidal excitation . Determine the response node-to-datum voltage v(t) in the steady state. (8)

b. The networks shown in Fig.9 (i) & Fig.9 (ii) have the identical graphs. Verify Tellegen’s theorem for these networks. (8)

Q.7 a. Write the properties of

(i) L-C imittance functions.

(ii) R-C impedance functions.

(iii) R-L impedance functions. (8)

b. (i) A coil having a 2 resistance is connected in series with a capacitor. The circuit resonates at 100 Hz. What is the inductance of the coil?

(ii) If the circuit is connected across a 100 V, 100 Hz ac source, find the power dissipated in the coil.

(iii) Calculate the voltages across the capacitor and the coil. (8)

Q.8 a. Show that when two 2-port networks and are connected in parallel, the equivalent Y-parameters of the combined network is the sum of Y-parameters of each individual 2-port network. (7)

b. Determine the h-parameters of the network shown in Fig.10. (9)

Q.9 Write notes on any TWO of the following:

(i) Properties of transfer function.

(ii) Chebyshev approximation.

(iii) Magnitude and frequency scaling. (16)