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Assignment # 0
Q1-Q10 Circuit Analysis
Q11-Q19 Mathematical Essentials
Q20 LTI
Instructions:
This is an INDIVIDUAL assignment. Every student must submit their own assignment (on proper A4 blank or lined page) with Name, Reg # and Section clearly marked on EACH page Questions must be done in sequence. Write the question Each Question must be finished before starting of next question, otherwise marks of that QUESTION will be deducted. (half the marks you get in that Question ) If you use internet or any book other than Norman S Nise, remember to provide reference in your work [IEEE format] Assignment deadline is : o Monday 29th^ January 2018 between 10.00 am and 10.15 am o At G#07 office o No assignments will be accepted after the deadline Pencil CANNOT be used Show all your workings CLEARLY Cheating/Plagiarism will result in severe consequences
Q-1 Find I 0 in the circuit in Figure 1 using mesh analysis
- Q-2 Using the loop analysis in figure 2, find V
- Q-3 Using Nodal Analysis confirm your answer to Q
- Q-4 Using Nodal Analysis confirm your answer to Q
- Q-5 Find Vx in the circuit shown in figure
Q-9 For the circuit in figure 7 draw input and output waveforms.
a) Vin = 10sin(2t) [Sine wave] b) Vin = 10u(t) [Unit Step] c) Vin = Triangular Wave [Magnitude 0-10V, Frequency 2 Hz] d) Vin = Square wave [Magnitude 0-10V, Frequency 2 Hz]
Q-10 For the circuit in figure 8 draw input and output waveforms.
a) Vi = 10sin(2t) [Sine wave] b) Vi = 10u(t) [Unit Step] c) Vi = Triangular Wave [Magnitude 0-10V, Frequency 2 Hz] d) Vi = Square wave [Magnitude 0-10V, Frequency 2 Hz]
Figure 7
Figure 8
Q11- Let 𝐴 = [
] , 𝐵 = [
] , 𝑎𝑛𝑑 𝐶 = [^1
]
a) Determine if matrices AB, AC, BC, CB, CBT^ exist. b) Compute BC. c) Compute ATA and AAT d) Compute C^2
Q-12 Let 𝐴 = [
] , 𝐵 = [
𝛽],
a) Give size of matrices: ATB and ABT b) Compute ATB c) Compute ABT
Q-13 Let 𝐴 = [
] , 𝐵 = [^2
]
a) Show that the inverse of B exists and compute the inverse of B. b) Find the inverse of A
Q-14 Let 𝐴 = [
] , 𝐵 = [
]
a) Show that A-1^ exists for any constant 𝜔 b) Use Cramer’s Rule to find the solution of Ax=B
Q-15 Compute all eigenvalues and their corresponding eigenvectors of the following matrices
a) 𝐴 = [
]
b) 𝐴 = [
]
Q-16 Show that 𝜆 = −5 is an eigenvalue of 𝐴 = [
] (Hint: show that
det(A+5I)=0)
Q-17 Let 𝐴 = [
] , 𝐹 = [1 −2], find AF
