The quantity of charge Q in coulombs (C) that has passed through a point in a wire up to time t (measured in seconds) is given by Q(t) = t3 – 2t2 + 6t + 2. Find the current when (a) t = 0.5 sand (b) t = 1 s. [See Example 3. The unit of current is an ampere (1 A = 1 C/s).) At what time is the current lowest?
EXAMPLE 3
FIGURE6
(a)
To find: The magnitude of current when the value of time is given as
Answer to Problem 19E
Therefore, the current when time
Explanation of Solution
Given:
The quantity of charge
The unit of current is in amperes (A).
Calculation:
Differentiate the equation (1) as below.
Calculate the current when
Substitute the value of
Therefore, the magnitude of current when time
(b)
To find: The magnitude of current when the value of time is given as
Answer to Problem 19E
The current when time
The current is lowest at the time equal to
Explanation of Solution
Calculate the current when time
Substitute the value
Therefore, the current when
Calculate at what time the current is lowest.
The current is lowest when the
Differentiate
Equating the
When the value of time
Substituting the value of
When the value of time
Substituting the value
Therefore, the current is lowest at the time
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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University Calculus: Early Transcendentals (3rd Edition)
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