(a) Explanation Given Information: In an electrical outlet the typical voltage supplied, V ( t ) = 165 cos ( 120 π t ) , where t is time in seconds in the United States. Formula Used: The total change of the function from x = a to x = b is, ∫ a b f ( x ) d x . Where, function f ( x ) is the rate of change of quantity. The formula for the integration of the function is, ∫ sin ( a x + b ) d x = − 1 a x + b cos ( a x + b ) + C , where the function is f ( x ) = sin ( a x + b ) , and a and b are constants, with a ≠ 0 . The average of a function f ( x ) on an interval [ a , b ] is given by f ¯ = 1 b − a ∫ a b f ( x ) d x . Constant multiple rule is ∫ k ⋅ g ( x ) d x = k ∫ g ( x ) d x where k is a constant. Calculation: Consider the provided function V ( t ) = 165 cos ( 120 π t ) . Determine the voltage over the interval [ 0 , 1 6 ] V ( t ) = ∫ 0 1 / 6 ( 165 cos ( 120 π t ) ) d t Then determine the average of a function F ( t ) on an interval [ a , b ] = [ 1 6 , 0 ] by applying the formula f ¯ = 1 b − a ∫ a b f ( x ) d x . V ¯ = 1 1 6 − 0 ∫ 0 1 / 6 ( 165 cos ( 120 π t ) ) d t = 6 ∫ 0 1 / 6 ( 165 cos ( 120 π t ) ) d t Now, evaluate the integral of the function by applying constant multiple rules and using shortcut formula of ∫ cos ( a x ) d x = 1 a sin ( a x ) + C to determine the position (b) To determine To graph: The function S ( t ) = ( V ( t ) ) 2 over the interval [ 0 , 1 6 ] . (c) To determine To calculate: The value of V r m s where the root mean square (RMS) voltage.

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

7th Edition

ISBN: 9781337291484

Author: Waner

Publisher: Cengage

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Chapter 16.3, Problem 67E

(a)

To determine

To calculate: The average voltage over the interval [0,16] and also estimate the number of times when the voltage reaches a maximum in 1 second.

(b)

To determine

To graph: The function S(t)=(V(t))2 over the interval [0,16].

(c)

To determine

To calculate: The value of Vrms where the root mean square (RMS) voltage.

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Chapter 16.3, Problem 66E

Chapter 16.3, Problem 68E

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Chapter 16 Solutions

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

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The average voltage over the interval [ 0 , 1 6 ] and also estimate the number of times when the voltage reaches a maximum in 1 second.

Solution Summary: The author calculates the average voltage over the interval left[0,16right] and the frequency of reaching the voltage to its maximum is 60 cycles per second.

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To calculate: The average voltage over the interval [0,16] and also estimate the number of times when the voltage reaches a maximum in 1 second.

To graph: The function S(t)=(V(t))2 over the interval [0,16].

To calculate: The value of Vrms where the root mean square (RMS) voltage.

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Chapter 16 Solutions