By Tony R. Kuphaldt
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Extra info for AC
1. INTRODUCTION 29 up to give a final answer: 5+3=8 8 5 0 1 2 3 3 4 5 6 ... 7 8 9 10 Later, we learned that there were ways to designate the values between the whole numbers marked on the line. 5 ... 0 1 2 3 4 5 6 7 8 9 10 Later yet we learned that the number line could extend to the left of zero as well: ... ) learned in grade school share a common trait: they’re all one-dimensional. The straightness of the number line illustrates this graphically. You can move up or down the number line, but all ”motion” along that line is restricted to a single axis (horizontal).
To represent these kinds of quantities, we need multidimensional representations. In other words, we need a number line that can point in different directions, and that’s exactly what a vector is. • REVIEW: • A scalar number is the type of mathematical object that people are used to using in everyday life: a one-dimensional quantity like temperature, length, weight, etc. • A complex number is a mathematical quantity representing two dimensions of magnitude and direction. • A vector is a graphical representation of a complex number.
Scalar numbers are the kind of numbers you’ve used in most all of your mathematical applications so far. The voltage produced by a battery, for example, is a scalar quantity. So is the resistance of a piece of wire (ohms), or the current through it (amps). However, when we begin to analyze alternating current circuits, we find that quantities of voltage, current, and even resistance (called impedance in AC) are not the familiar one-dimensional quantities we’re used to measuring in DC circuits. Rather, these quantities, because they’re dynamic (alternating in direction and amplitude), possess other dimensions that must be taken into account.
AC by Tony R. Kuphaldt