MU Circuit Theory - December 2015 Exam Question Paper

MU Electronics Engineering (Semester 3)
Circuit Theory
December 2015

Total marks: --
Total time: --

INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1 (a) The constants of a transmission lines are R=6/km, L=2.2mH/km
G=0.25×10^-6 mho/km C=0.005×10^-5 F/km
Determine the characteristic impedance propagation constant phase constant and attenuation constant at 1 KHz.

5 M

1 (b) Obtain the expression for i(t) if switch is closed at t=0 If v(t) is i(t) = ramp signal

5 M

1 (c) Check whether the polynomial is Hurwitz or not by continued fraction method. F(S)=S⁴+S³+4S²+2S+3.

5 M

1 (d) Find out

\frac{V_{2}}{V_{1}}

$\dfrac {V_2}{V_1}$ for the following n/w given below.

5 M

2 (a) Find the voltage across 5Ω resistor in the network shown below. If K=0.8 is coefficient of coupling.

8 M

2 (b) In the circuit shown, find out the expression for voltage V(t) across capacitor for t>0 At t=0 Switch is closed.

8 M

2 (c) Define ABCD parameters for the two port network hence obtain condition for symmetry.

4 M

3 (a) Find

i, \frac{d i}{d t} and \frac{d^{2} i}{d t^{2}} at t = 0^{+}

$i, \ \dfrac {di}{dt} \text{ and }\dfrac {d^2i}{dt^2} \text{ at }t=0^+$ in the circuit given below. Switch is changed from position 1 to 2 at t=0.

6 M

3 (b) Compare and Obtain Foster I and Foster II of the following RC impedance function.

Z (S) = \frac{2 (S + 2) (S + 4)}{(S + 1) (S + 3)}

$Z(S) = \dfrac {2 (S+2)(S+4)}{(S+1)(S+3)}$

8 M

3 (c) Obtain Cauer form I of LC network

Z (s) = \frac{(s^{2} + 4) (s^{2} + 16)}{s (s^{2} + 9)}

$Z(s)= \dfrac {(s^2+4)(s^2+16)}{s(s^2+9)}$

6 M

4 (a) Derive the characteristic equation of a transmission line also obtain α β γ of the transmission line.

8 M

4 (b) Derive the relation for nominal impedance and cut off frequency for a constant k low pass filter.

4 M

4 (c) A network and its pole zero diagram are shown in fig. Determine the values of R, , C if Z(0)=1.

8 M

5 (a) Check whether the following functions are PRF or not

i) F (s) = \frac{S (S + 3) (S + 5)}{(S + 1) (S + 4)} i i) F (S) = \frac{S^{3} + 6 S^{2} + 7 S + 3}{S^{2} + 2 S + 1}

$i) \ F(s) = \dfrac {S(S+3)(S+5)}{(S+1)(S+4)} \\ ii) \ F(S) = \dfrac {S^3+6S^2 + 7S +3}{S^2 + 2S+1}$

8 M

5 (b) Find the current I_x using superposition theorem.

6 M

5 (c) The current

I (S) = \frac{2 S}{(S + 1) (S + 2)}

$I(S) = \dfrac {2S}{(S+1)(S+2)}$ plot the pole zero pattern in s-plane hence obtain i(t) by finding out residues by graphical method.

6 M

6 (a) The characteristics impedance of a high frequency line is 100Ω. If it is terminated by a load impedance of 100 +j100Ω. Using smith chart find out (i) VSWR
(ii) Refection coefficient (iii) Impedance at

\frac{1}{10}

$\dfrac {1}{10}$ of wavelength away from load (iv) VSWR minimum and VSWR maximum away from the load.

8 M

6 (b) For the network shown and find out

\frac{v_{1}}{I_{1}} and \frac{v_{2}}{I_{1}}

$\dfrac {v_1}{I_1} \text{ and } \dfrac {v_2}{I_1}$

6 M

6 (c) Find out Thevenin's equivalent network.

6 M

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