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Phasor Mathematics
13 questions By Tony R. Kuphaldt
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Question 1 of 13
Provide a definition for phasor, as the term applies to electrical calculations.
Reveal answerA “phasor” is a complex-number representation of an electrical quantity, such as voltage, current, or impedance.
Notes:The ingredient of complex must be present in any definition of a phasor. A phasor, while it may be classified as a type of vector (possessing both magnitude and direction), is not the same as the vectors commonly used in other areas of physics (e.g. force vectors, electric/magnetic field vectors, etc.).
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Question 2 of 13
A series is a very important concept in mathematics. The common notation for a “series” looks something like this (a type of “geometric” series is shown here as an example):
$$\sum_{n=0}^\infty x^n$$
Explain what this notation means, and how we may approximate the value of a series for a finite value of n.
Reveal answerA “series” is comprised of a set of terms added together, each term related to the others by a common form, distinguished only by the incrementing or decrementing of a common variable. To illustrate by example, here is an expansion of the geometric series shown in the question:
$$\sum_{n=0}^\infty x^n = x^0+x^1+x^2+x^3+x^4+...+x \infty$$
Follow-up question: what do you think the value of this series would be if the value of x was greater than (positive) 1? What if x = 0? What if 0 < x < 1?
Notes:The purpose of this question is to familiarize students with the concept of a mathematical series, and the notation used to describe series.
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Question 3 of 13
A common mathematical function known as factorial is represented by an exclamation point following a positive integer number. The following are all examples of factorials:
1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 6! = 720 Explain in your own words what this “factorial” function represents. What procedure (algorithm) would we use to arithmetically calculate the value of any factorial given to us?
Reveal answerI’ll let you research this on your own! The algorithm isn’t that difficult to figure out just by examining the sequence of factorials given in the question.
Follow-up question: calculate 0!
Notes:In addition to being very useful in probability calculations, factorials are frequently seen in important mathematical series, including those used to calculate e, sin, and cos.
