Electrical and Telecommunications Engineering Final Examination

Question 1 -

(a) Find current i(t) in Figure 1.

(b) Find current phasors I₁, I₂ and I₃ in the circuit of Figure 2. Draw a phasor diagram of these currents to show that I₁ = I₂ + I₃.

(c) Consider the Figure 3 below. Find the value of capacitance C such that v(t) and i(t) are in phase when frequency is 80 Hz.

Question 2 -

(a) For the circuit in Figure 4, the current source is i_s(t) = 6 cos 10³t and loads are 10 Ω and 20 mH.

(i) Find the average power, reactive power and apparent power absorbed in the load.

(ii) What impedance should replace the load for maximum power transfer?

(iii) What is the average power absorbed in the new impedance of (ii)?

(b) What is a quality factor Q of a resonance circuit? Show that at resonance in a series resonance circuit, voltage across the capacitor V_c is the product of Q and source voltage V_s i.e.  V_c = QV_s.

(c) Figure 5 shows a RLC series resonant circuit. This circuit was designed for a resonance frequency f = 1000 Hz and quality factor Q = 200. An inductor L of value 0.02 H is selected. The resistor R in the circuit is simply the internal resistance of the selected inductor.

(i) What value of capacitor C should be selected?

(ii) What is the value of R?

(iii) What should be the voltage rating V_C of the selected capacitor?

Question 3 -

(a) Find voltage V_x in the Figure 6.

(b) If the switch in Figure 7 has been closed for a long time before it is opened at t = 0, determine-

(i) the characteristic equation of the circuit,

(ii) current i_x for t > 0

Question 4 -

(a) Find the impedance (z) parameters for the two-port network given in Figure 8.

(b) Find the Fourier series of the function f(t) below in Figure 9, up to the first four terms.

(c) Find the Fourier transform of the function f(t) below in Figure 10.

Question 5 -

(a) Suppose a circuit with input x(t) and output y(t) is analysed, and the following differential equation is obtained:

d²y(t)/dt² + 3(dy(t)/dt) + 2 y(t) = x(t)

subject to the initial conditions y(0) = 2 and dy(0)/dt = -1.

Using Laplace transforms,

i) Find the poles and zeroes of this circuit, and plot them on the s-plane.

ii) Solve for the output y(t) if the input is x(t) = 4e^-3tu(t) , where u(t) is the unit step function.

(b) Consider the circuit in Figure 11.

iii) For the circuit shown in Fig. 11, derive the transfer function H(s) = V_out(s)/V_in(s), showing working.0

iv) Hence, or otherwise, sketch the magnitude response |H(jω)|, showing the values of at least two points on the response.

 v) Using Laplace transforms, and showing all working, derive an expression for the output v_out(t) , if the input voltage is v_in(t) = cos(2t)u(t) V, where u(t) is the unit step function.

Attachment:- Assignment File.rar