## Circuits and Networks - May 2015

### Electronics and Comm. Engg. (Semester 3)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1 (a)** Explain the terms: (i) Linear (ii) Bilateral (iii) Passive (iv) Reciprocal (v) Time invariant (vi) Oriented graph and (vii) Tree.(7 marks)
**1 (b)** Justify: the current in an inductor and voltage across a capacitor cannot change instantaneously.(7 marks)
**2 (a)** State and explain maximum power transfer theorem. Also derive the condition for maximum power transfer to the load for DC and AC circuit.(7 marks)

### Answer any one question from Q2 (b) & Q2 (c)

**2 (b)** Using mesh analysis determine mesh current i and the value of k which causes i=0 if V_{1} =10 v and V_{2}=2 v for the network shown in figure 1.
(7 marks)
**2 (c)** Using nodal analysis find the value of k such that V y is zero for the network shown in figure 2.
(7 marks)

### Answer any two question from Q3 (a), (b) & Q3 (c), (d)

**3 (a)** What is significance of initial condition? Write initial conditions for R, L and C at t=0 + and at t=∞.(7 marks)
**3 (b)** For the network shown in figure 3 the switch k is closed at t=0, also it reaches a steady state with the switch k open. Find the current i(t) for all time.
(7 marks)
**3 (c)** What is time constant? Explain time constant in terms of RL and RC circuit.(7 marks)
**3 (d)** Determine V_{b} (0_{+}) and V_{b} (∞) for the network shown in figure 4, which reaches to steady state with switch k open and at t=0, the switch k is closed.
(7 marks)

### Answer any two question from Q4 (a), (b) & Q4 (c), (b)

**4 (a)** Explain concept of poles and zeros and their significance in network functions.(7 marks)
**4 (b)** Find the h parameters for the network shown in figure 5.
(7 marks)
**4 (c)** Find Laplace transform of f_{1}(t)=cos ωt and f_{2}(t)=e^{-at} sin ωt.(7 marks)
**4 (d)** For the network shown in figure 6 determine voltage transfer gain G_{12} =V_{2}/V_{1}.
(7 marks)

### Answer any two question from Q5(a), (b) & Q5 (c), (d)

**5 (a)** Derive relationship between incidence matrix (A), fundamental cut-set matrix (Q_{f}) and fundamental tie-set matrix (B_{f}).(7 marks)
**5 (b)** Find the Z parameters for the network shown in figure 7.
(7 marks)
**5 (c)** Derive expression of h parameter in terms of Z and Y parameters.(7 marks)
**5 (d)** For the network shown in figure 8 draw the oriented graph. Also obtain incidence matrix (A), fundamental tie-set matrix (B_{f}) and fundamental cut-set matrix (Q_{f}).
(7 marks)