Learning Resource Topics Overview 1 Charge & Coulomb’s Law 2 Electric Current 3 Voltage 4 Resistance 5 Ohm’s Law 6 Power & Energy 7 Elements of Electric Circuits 8 Kirchhoff’s Law 9 Series Circuits 10 Parallel Circuits 11 Analysis of Combination Circuits 12 Capacitance 13 Inductance

Scalar and Vector

Scalar is a quantity which is fully described by a magnitude alone. For example, when length is measured, the quantity that results is called a scalar. Vector is a quantity which is fully described by both magnitude and direction.

Basic Laws of Vector Algebra

A vector A can be written as

 (1.4)

Where A is the magnitude of the vector A,

 (1.5)

and â is the unit vector which has a magnitude of unity (|â|=1), and its direction is given by

 (1.6)

The unit vector in the direction of the x-axis is i and the unit vector in the direction of the y-axis is j.

The vector A can be represented graphically by a directed straight-line segment of a length |A| = A with its arrowhead pointing in the direction of â as shown in Figure 1.2

Figure 1.2 A vector quantity with magnitude and direction.

Force as an example of a Vector

A force (F) is a vector quantity. To fully describe the force acting upon an object, you must describe both the magnitude (size) and the direction. Thus, the quantity 5 newtons (N) is not a full description of the force acting upon an object. In contrast, saying “5 N upwards” is a full description of the force acting upon an object; both the magnitude (5 N) and the direction (upwards) are given. It is common to use special notation for vector quantities. For example F is used for the force and |F| for the magnitude of force. Table 1.1 classifies few common quantities.

Table 1.1 Classification of Common Quantities

Content and Pedagogy© 2004, University of Ottawa, Faculty of Engineering and Faculty of Education
Design and Production © 2004, University of Ottawa, Centre for e-Learning