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Active Learning Assignments

Active Learning Assignments. Department - ELECTRONICS & COMMUNICATION( 1 ) Subject - ELEMENTS OF ELECTRICAL ENGINEERING Members: Name Id no TOUSHI JHA 13BEECM028

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Active Learning Assignments

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  1. Active Learning Assignments Department -ELECTRONICS & COMMUNICATION(1) Subject - ELEMENTS OF ELECTRICAL ENGINEERING Members: Name Id no TOUSHI JHA 13BEECM028 SHIVANI BADGUJAR 13BEECG004 KRUTI SHAH 13BEECF001 ARCHANA PRADHAN 13BEECMO34 Guided Teacher - PRIYANKA THAKRE

  2. VECTORS

  3. VECTOR BASICS Images: http://www.physicsclassroom.com/Class/vectors/u3l1a.cfm

  4. VECTOR REPRESENTATION 1. The length of the line represents the magnitude and the arrow indicates the direction. 2. The magnitude and direction of the vector is clearly labeled.

  5. PROPERTIES OF VECTORS • Vectors can be moved parallel to themselves in a diagram. • Vectors can be added in any order. For example, A + B is the same as B + A • To subtract a vector, add its opposite. SIGNS (DIRECTION) ARE VERY IMPORTANT!!! • Multiplying or dividing vectors by scalars results in vectors. For example: When you divide displacement (x or  y) by time (s) the result is velocity (v).

  6. Adding Vectors by Components • Adding vectors: • Draw a diagram; add the vectors graphically. • Choosex and y axes. • Resolve each vector into x and ycomponents. • Calculate each component using sines and cosines. • Add the components in each direction. • To find the length and direction of the vector, use:

  7. 100 N 75 N 75 N 100 N Addition of Vectors-Sample Problems • First you should have sketched the situation. • Second you should have moved the vectors to either add them by the parallologram or head to tail method. Shown here is the head to tail method.

  8. Adding Vectors by Components 1.3.3 Resolve vectors into perpendicular components along chosen axes. Any vector can be expressed as the sum of two other vectors, which are called its components. Usually the other vectors are chosen so that they are perpendicular to each other.

  9. Adding Vectors by Components If the components are perpendicular, they can be found using trigonometric functions.

  10. Adding Vectors by Components The components are effectively one-dimensional, so they can be added arithmetically:

  11. Addition of Vectors – Graphical Methods The parallelogram method may also be used; here again the vectors must be “tail-to-tip.”

  12. Addition of Vectors – Graphical Methods • Parallelogram method: • It is commonly used when you have concurrent vectors. • The original vectors make the adjacent sides of a parallelogram. • A diagonal drawn from their juncture is the resultant. • Its magnitude and direction can be measured.

  13. PARALLALOGRAM METHOD • Find the resultant force vector of the two forces below. • 25 N due East, 45 N due South 25 N, East Decide on a scale!!! 51 N 59º S of E 51 N 31º E of S 45 N, South

  14. Addition of Vectors – Graphical Methods • Graphically find the sum of these two vectors using the head to tail method. A B

  15. B’ A B Addition of Vectors – Graphical Methods • First, vector B must be moved so it’s tail is at the head of vector A. • All you do is slide vector B to that position without changing either its length (magnitude) or direction. • The new position of vector B is labeled B’ in the diagram.

  16. A’ B’ A B Addition of Vectors – Graphical Methods • Next, vector A must be moved so it’s tail is at the head of vector B. • All you do is slide vector A to that position without changing either its length (magnitude) or direction. • The new position of vector A is labeled A’ in the diagram.

  17. A’ B’ R A B Addition of Vectors – Graphical Methods • The resultant vector is then drawn from the point where the two vectors were joined to the opposite corner of the parallelogram. • This resultant is labeled R in the diagram.

  18. A’ B’ R A B Zero Addition of Vectors – Graphical Methods • The magnitude of the resultant can then be measured with a ruler and the direction can be measured with a protractor. • The zero of the protractor should be located at the point labeled zero on the diagram

  19. Addition of Vectors – Graphical Methods When two or more vectors (often called components) are combined by addition, or composition, the single vector obtained is called the resultant of the vectors • The sum of any two vectors can be found graphically. • There are two methods used to accomplish this: head to tail and parallelogram. • Regardless of the method used or the order that the vectors are added, the sum is the same.

  20. Addition of Vectors – Graphical Methods Even if the vectors are not at right angles, they can be added graphically by using the “tail-to-tip” method.

  21. Addition of Vectors – Graphical Methods • Head to tail method • The tail of one vector is placed at the head on the other vector. • Neither the direction or length of either vector is changed. • A third vector is drawn connecting the tail of the first vector to the head of the second vector. • This third vector is called the resultant vector. • Measure its length to find the magnitude then measure its direction to fully describe the resultant

  22. A B Addition of Vectors – Graphical Methods • Graphically find the sum of these two vectors using the head to tail method.

  23. B’ A B Addition of Vectors – Graphical Methods • First, vector B must be moved so it’s tail (the one without the arrow point) is at the head (the one with the arrow point) of vector A. • All you do is slide vector B to that position without changing either its length (magnitude) or direction. • The new position of vector B is labeled B’ in the diagram.

  24. B’ R A B Addition of Vectors – Graphical Methods • The resultant vector is drawn from the tail of vector A to the head of vector B and is labeled R.

  25. B’ R A B Zero Addition of Vectors – Graphical Methods • The magnitude of the resultant can then be measured with a ruler and the direction can be measured with a protractor. • The zero of the protractor should be located at the point labeled zero on the diagram

  26. Subtraction of Vectors, and Multiplication of a Vector by a Scalar A vector V can be multiplied by a scalarc; the result is a vector cV that has the same direction but a magnitudecV. If c is negative, the resultant vector points in the opposite direction. Multiplication and division of vectors by scalars is also required.

  27. Subtraction of Vectors, and Multiplication of a Vector by a Scalar In order to subtract vectors, we define the negative of a vector, which has the same magnitude but points in the opposite direction. Then we add the negative vector:

  28. MULTIPLICATION OF VECTORS

  29. In mathematics, Vector multiplication refers to one of several techniques for the multiplication of two (or more) vectors with themselves. It may concern any of the following : Dot product — also known as the "scalar product", an operation which takes two vectors and returns a scalar quantity. Cross product — also known as the "vector product", a binary operation on two vectors that results in another vector.

  30. THANK YOU

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