1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
DIA [1.3K]
3 years ago
9

Suppose you want to find the sum of two sinusoidal voltages, given as follows: v1(t)=V1 cos(ωt+ϕ1) and v2(t)=V2 cos(ωt+ϕ2)v1(t)=

V1 cos(ωt+ϕ1) and v2(t)=V2 cos(ωt+ϕ2).
If you stay in the time domain, you will have to use trigonometric identities to perform the addition. But if you transform to the frequency domain, you can simply add the phasors V1V1 and V2V2 as complex numbers using your calculator. Your answer will be a phasor, so you will need to inverse phasor-transform it to get the answer in the time domain. This is an example of a problem that is easier to solve in the frequency domain than in the time domain.

Use phasor techniques to find an expression for v(t) expressed as a single cosine function, where v(t)=[100cos(300t+45∘)+500cos(300t−60∘)] V. Enter your expression using the cosine function. Round real numbers using two digits after the decimal point. Any angles used should be in degrees.

Engineering
2 answers:
nydimaria [60]3 years ago
5 0

Answer:

Rectangular form V = 320.71 - j362.3

Polar form V = 483.85 < -48.48°

Phasor form V = 483.85cos(300t - 48.48°)

Explanation:

We are given a sinusoidal function

V(t) = 100cos(300t + 45°) + 500cos(300t - 60°)

We are required to find the v(t) expressed as a single cosine function using phasor technique.

In polar form,

100cos(300t + 45°) = 100 < 45°

500cos(300t - 60°)  = 500 < -60°

In rectangular form,

100 < 45° = 70.71 + j70.71

500 < -60° = 250 - j433.01

Adding the two signals

(70.71 + j70.71) +  (250 - j433.01)

In rectangular form,

V = 320.71 - j362.3

In polar form

V = 483.85 < -48.48°

Therefore, the answer is  

in rectangular form V = 320.71 - j362.3

in polar form V = 483.85 < -48.48°

in phasor form V = 483.85cos(300t - 48.48°)

Conversion from Rectangular to Polar form:

V = X + jY to Magnitude < Angle

V = 320.71 - j362.3

Magnitude = \sqrt{(320.71)^2 +(362.3)^2} = 483.85

Angle = tan⁻¹(Y/X) = tan⁻¹(-362.3/320.71) = -48.48°

V = 483.85 < -48.48°

Conversion from Polar to Rectangular form:

V = 483.85 < -48.48°

X =  Magnitude*cos(Angle) and jY = Magnitude*sin(Angle)

X = 483.85*cos(-48.48°) and jY = 483.85*sin(-48.48°)

X = 320.71 and jY = -362.3

V = 320.71 - j362.3

seropon [69]3 years ago
3 0

Answer:

Attached is the full solution.

You might be interested in
What is the sun's degree angle in the sky in summer and in winter?
Vladimir [108]

Answer:

At the time of the summer or winter solstices, the Sun is 23.44° degrees above or below the horizon, respectively, irrespective of time of day.

Explanation:

6 0
2 years ago
What is the activation energy (Q) for a vacancy formation if 10 moles of a metal have 2.3 X 10^13 vacancies at 425°C?
Yakvenalex [24]

Answer:

Activation\ Energy=2.5\times 10^{-19}\ J

Explanation:

Using the expression shown below as:

N_v=N\times e^{-\frac {Q_v}{k\times T}

Where,

N_v is the number of vacancies

N is the number of defective sites

k is Boltzmann's constant = 1.38\times 10^{-23}\ J/K

{Q_v} is the activation energy

T is the temperature

Given that:

N_v=2.3\times 10^{13}

N = 10 moles

1 mole = 6.023\times 10^{23}

So,

N = 10\times 6.023\times 10^{23}=6.023\times 10^{24}

Temperature = 425°C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15  

So,  

T = (425 + 273.15) K = 698.15 K  

T = 698.15 K

Applying the values as:

2.3\times 10^{13}=6.023\times 10^{24}\times e^{-\frac {Q_v}{1.38\times 10^{-23}\times 698.15}

ln[\frac {2.3}{6.023}\times 10^{-11}]=-\frac {Q_v}{1.38\times 10^{-23}\times 698.15}

Q_v=2.5\times 10^{-19}\ J

4 0
3 years ago
An Ideal gas is being heated in a circular duct as while flowing over an electric heater of 130 kW. The diameter of duct is 500
max2010maxim [7]

Answer: The exit temperature of the gas in deg C is 32^{o}C.

Explanation:

The given data is as follows.

C_{p} = 1000 J/kg K,   R = 500 J/kg K = 0.5 kJ/kg K (as 1 kJ = 1000 J)

P_{1} = 100 kPa,     V_{1} = 15 m^{3}/s

T_{1} = 27^{o}C = (27 + 273) K = 300 K

We know that for an ideal gas the mass flow rate will be calculated as follows.

     P_{1}V_{1} = mRT_{1}

or,         m = \frac{P_{1}V_{1}}{RT_{1}}

                = \frac{100 \times 15}{0.5 \times 300}

                = 10 kg/s

Now, according to the steady flow energy equation:

mh_{1} + Q = mh_{2} + W

h_{1} + \frac{Q}{m} = h_{2} + \frac{W}{m}

C_{p}T_{1} - \frac{80}{10} = C_{p}T_{2} - \frac{130}{10}

(T_{2} - T_{1})C_{p} = \frac{130 - 80}{10}

(T_{2} - T_{1}) = 5 K

T_{2} = 5 K + 300 K

T_{2} = 305 K

           = (305 K - 273 K)

           = 32^{o}C

Therefore, we can conclude that the exit temperature of the gas in deg C is 32^{o}C.

7 0
3 years ago
Income tax payable is included in the account...​
den301095 [7]

Answer:

Current Liabilities

Explanation:

Accounts of Current Liabilities

  • Account Payable
  • Expense Payable
  • Tax Outcome
  • Tax Income
  • Income tax payable
5 0
2 years ago
Read 2 more answers
Q4 a.
dedylja [7]

The Java program that accepts a matrix of M × N order and then interchanges diagonals of the matrix is given below:

<h3>Steps:  </h3>
  • 1. We can only interchange diagonals for a square matrix.
  • 2. Therefore, we would have to create a square matrix of size [M × M].
  • 3. We would check whether the matrix is a square matrix or not. If the matrix is square then follow step 3 else terminate the program.
  • 4. Apply logic for interchange diagonal of the matrix some logic is given below.

<h3>Java Code</h3>

//  Java Program to Accept a Matrix of Order M x N &

//  Interchange the Diagonals

import java.util.Scanner;

public class InterchangeDiagonals {

   public static void main(String[] args)

   {

       // declare variable

       int m, n, i, j, temp;

       // create a object of scanner class

       Scanner sc = new Scanner(System.in);

       System.out.print("Enter number of rows ");

       // take number of rows

       m = sc.nextInt();

       System.out.print("Enter number of columns ");

       // take number of columns

       n = sc.nextInt();

       // declare a mxn order array

       int a[][] = new int[m][n];

       // if block it's execute when m is equals to n

       if (m == n) {

           System.out.println(

               "Enter all the values of matrix ");

           // take the matrix inputs

           for (i = 0; i < m; i++) {

               for (j = 0; j < n; j++) {

                   a[i][j] = sc.nextInt();

               }

           }

           System.out.println("original Matrix:");

           // print the original matrix

           for (i = 0; i < m; i++) {

               for (j = 0; j < n; j++) {

                   System.out.print(a[i][j] + " ");

               }

               System.out.println("");

           }

          // perform interchange

           for (j = 0; j < m; j++) {

               temp = a[j][j];

               a[j][j] = a[j][n - 1 - j];

               a[j][n - 1 - j] = temp;

           }

           System.out.println(

               " after interchanging diagonals of matrix ");

           // print interchanged matrix

           for (i = 0; i < m; i++) {

               for (j = 0; j < n; j++) {

                   System.out.print(a[i][j] + " ");

               }

               System.out.println("");

           }

       }

       // else block it's only execute when m is not equals

       // to n

       else {

           System.out.println("Rows not equal to columns");

       }

   }

}

Read more about java programming here:

brainly.com/question/18554491

#SPJ1

7 0
1 year ago
Other questions:
  • Five bolts are used in the connection between the axial member and the support. The ultimate shear strength of the bolts is 320
    5·1 answer
  • Which of the following is not a primary or fundamental dimension? (a)-mass m (b)-length L (c)- timer t (d)-volume V
    5·1 answer
  • An aluminium alloy tube has a length of 750 mm at a temperature of 223°C. What will be its length at 23°C if its coefficient of
    7·1 answer
  • Why is concrete on its own not a good material to use
    6·1 answer
  • ____ technologies are new technologies that are not currently widely employed.
    15·2 answers
  • The Greek alphabet has 24 distinct lowercase letters. How many bits are needed to be able to encode any single lowercase Greek l
    9·1 answer
  • the frequencies 10, 12, 23 and 45 Hz. (a) What is the minimum sampling rate required to avoid aliasing? (b) If you sample at 40
    13·1 answer
  • Compare the temperature dependence of Nabarro-Herring and Coble creep. Which is more temperature-sensitive
    15·1 answer
  • Basic C++ For Loop I'm trying to learn. Replit tells me that the for in the forloop is an error, but I don't know what's wrong.
    7·1 answer
  • 9. An automobile's oxygen sensor output needs
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!