Reference no: EM131514521
Circuits and Signals - Final Examination
Question 1-
(a) In a linear circuit voltage across and current through the total impedance are given as
v(t) = 50 cos(10t + 10o) V and i(t) = 25 cos(10t + 41o) A.
Is the total impedance Z of the circuit inductive or capacitive? Explain your answer.
(b) At ω = 314 rad/s, the equivalent admittance Y for the circuit in Figure 1 is (0.32 + j0.64) mS. Calculate values of R and C.
![2322_figure.png](https://secure.expertsmind.com/CMSImages/2322_figure.png)
(c) Find the source voltage vs in the circuit of Figure 2 if the current I, through the 1-? resistor is (0.5 sin 200t) A.
![2251_figure1.png](https://secure.expertsmind.com/CMSImages/2251_figure1.png)
(d) Determine current i(t) in the circuit of Figure 3 which have two voltage sources of two different frequencies.
![797_figure2.png](https://secure.expertsmind.com/CMSImages/797_figure2.png)
Question 2 -
(a) Calculate the value of impedance ZL in the circuit of Figure 4 in order for ZL to receive maximum average power. What is the maximum average power received by ZL when Thevenin's equivalent voltage across the terminals of ZL is given as VTh = (10+j70) V?
![728_fiugure3.png](https://secure.expertsmind.com/CMSImages/728_fiugure3.png)
You may use Pmax = |VTh|2/8RL to calculate maximum average power.
(b) In the circuit of Figure 5 device A receives 2 kW at 0.8 pf lagging, device B receives 3 kVA at 0.4 pf leading, while device C is inductive and consumes 1 kW and re 500VAR.
(i) Determine the power factor of the entire system.
(ii) Find current I (rms) given that Vs = 120∠45o V (rms).
![1752_figure4.png](https://secure.expertsmind.com/CMSImages/1752_figure4.png)
(c) (i) Discuss mutual inductance M and its effects in two magnetically coupled coils.
(ii) For the coupled coils in Figure 6 show that equivalent inductance is
Leq = (L1L2 - M2)/(L1 + L2 - 2M)
![2333_figure5.png](https://secure.expertsmind.com/CMSImages/2333_figure5.png)
Question 3 -
(a) If the switch in Figure 7 has been closed for a long t me before it is opened at t = 0, determine-
(i) the characteristic equation of the circuit,
(ii) ix for t > 0
![488_figure6.png](https://secure.expertsmind.com/CMSImages/488_figure6.png)
You may take help of following formula:
Over-damped case: i(t) or v(t) = A1es_1t + A2es_2t , where s1,2 = -α ± √(α2 - ω02)
Critically damped case: i(t) or v(t) = (A2 + A1t)e-αt, where s1,2 = - α
Under damped case: i(t) or v(t) = e-αt(B1cosωdt + B2sinωdt), where ωd = √(ω02 - α2)
(b) For the network given in Figure 8,
(i) Draw the equivalent s-domain circuit. Assume at t < 0 voltage and current in the circuit are zero.
(ii) Write the mesh analysis equations of the circuit in s-domain.
(iii) Comment on difference between s domain (Laplace transformation) and frequency domain (phasors) analysis.
![1574_figurre7.png](https://secure.expertsmind.com/CMSImages/1574_figurre7.png)
(c) A circuit is known to have its transfer function as,
H(s) = (s + 3)/(s2 + 4s + 5)
Find its output in time domain when the input is a unit step function u(t).
You may use Laplace transformation tables provided at the back of the question paper.
Question 4 -
(a) (i) What are the half power frequencies in a resonant circuit? Explain with help of a sketch, labelling all the important points.
(ii) Starting from the condition of half power |Z| = √2R, express the two half power frequencies ω1 and ω2 in terms of circuit parameters R, Land C of a series resonant circuit.
(iii) Show that bandwidth B in a series RLC resonant circuit is R/L.
(iv) If a series RLC circuit has B = 8 rad/s and resonance frequency ωo = 1,500 rad/s and R = 10 Ω, find values of L and C.
(v) Also find the quality factor Q of the circuit defined in part (iv).
(b) Show that the trigonometric Fourier series expansion of the backward sawtooth waveform of Figure 9 is f(t) = 5 + 10/π n=1∑∞ 1/n sin(nπt)
![776_fiugre8.png](https://secure.expertsmind.com/CMSImages/776_fiugre8.png)
(c) Find the response v0(t) of the circuit of Figure 10 when the voltage source vs(t) is given by the backward sawtooth waveform f(t) of Figure 9.
![213_figure9.png](https://secure.expertsmind.com/CMSImages/213_figure9.png)
Attachment:- Assignment File.rar