Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Textbook Question
Chapter 5.6, Problem 43E
Electric Generator The graph shows an oscilloscope reading of the variation in voltage of an AC current produced by a simple generator.
- (a) Find the maximum voltage produced.
- (b) Find the frequency (cycles per second) of the generator.
- (c) How many revolutions per second does the armature in the generator make?
- (d) Find a formula that describes the variation in voltage as a function of time.
(a)
Expert Solution
To determine
The value of maximum voltage produced by the generator.
Explanation of Solution
The graph which shows the variation of voltage of an AC current produced by a simple generator is given below.
Figure (1)
From the Figure (1), it is noticed that the maximum voltage of the curve lies on the y-axis at 45.
Thus, the value of maximum voltage is
(b)
Expert Solution
To determine
The frequency of the generator.
Explanation of Solution
The graph for the voltage is variation is given below.
Figure (1)
From the Figure (1) it is noticed that the period of the sine curve is
Thus, the frequency of the sine curve is defined as,
(c)
Expert Solution
To determine
The number of revolution per second the armature takes in the generator.
Explanation of Solution
The one revolution of the armature generates one cycle of voltage.
The frequency of the voltage is
So, the value of one revolution of armature is
(d)
Expert Solution
To determine
The formula that describes the variation in voltage as a time function.
Explanation of Solution
The graph for the voltage is variation is given below,
Figure (1)
From the Figure (1) it is noticed that the period of the sine curve is
Since the waves starts from positive 45 then, the formula of frequency,
Substitute 40 for f in the above formula,
The general equation for simple harmonic motion is,
Substitute
Thus the general formula of voltage variation is
Chapter 5 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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