Reference no: EM133289867

Question 1:

The following figure 1 shows a circuit of N number of loops with series resistance (R_s1,R_s2, ...., R_sn) and parallel resistance (R_p1,R_p2,... . , R_pn).

Write a function in MATLAB to determine the A matrix for 5 loops. Once the function is scripted, write a separate MATLAB code to call the A matrix from the function and determine the nodal voltage at each point.  Given: 

Series Resistance (Rs) = 4Ω; All the series resistances are of equal value.

Parallel Resistance (Rp) = 6Ω; All the parallel resistances are of equal value.

Reference Voltage (V_ref) = 30V. 

Figure 1: A circuit with N number of loops

Question 2: 

Write a function in MATLAB code to calculate the probability of getting each number of a dice by throwing it N number of times. The number observed would be decided by generating a random number, such that:

If the random number chosen is 

a)      between 0-0.2, then number observed is 1.

b)      between 0.2-0.4, then number observed is 2.

c)       between 0.4-0.5, then number observed is 3.

d)      between 0.5-0.7, then number observed is 4.

e)      between 0.7-0.9, then number observed is 5.

f)       between 0.9-1.0, then number observed is 6. 

The number of throws considered are:

1.      1000 times

2.      100000 times

3.      10000000 times

i) Once the function is scripted, created a separate script in MATLAB to call the function and determine the probability of each number. The input argument to the function would be Number of throws and the output argument would be probability of each number.  

ii) Is the sum of the probabilities equal to one? 

Question 3:

Given a DTMF signal, where the frequency of the signal will be decided on the number typed between 09, the total period of the signal is 1 second. Create a function first to call any number between 0-9 and generate its two frequencies. 

Create a separate MATLAB script to call the function to generate frequencies of any number. The amplitude of the signal is 100, such that the signal will be on for certain intervals and off for the remaining period. The signal is on for the following duration:

i. 0.4 second  

ii. 0.6 second

iii. 0.8 second

Generate and plot noise with mean 0 and variance 1 and explain the signal plot you received in frequency domain.

Question 4:

Determine the value of x when the following functions are zero:

a. f(x) = x² + 4x - 2

b. f(x) = 3x² + 5x - 10

c. f(x) = 5x - 1

1. Write a flow-chart for the process.

2. Take an appropriate step-size.

3. Determine the number of iterations and the time taken for the following tolerance value:

i) 0.1

ii) 0.01

iii) 0.001

4. What is the percentage difference of x values obtained from ii) and iii) with respect to i).