BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.8, Problem 19E

(a)

To determine

To find: The magnitude of current when the value of time is given as t=0.5s, also the time at which the lowest value of current occurs.

Expert Solution

Answer to Problem 19E

Therefore, the current when time t is equal to 0.5s is 4.75A.

Explanation of Solution

Given:

The quantity of charge Q in coulombs (C) that has passed through a point in wire up to time t is given by the equation

Q(t)=t32t2+6t+2 (1)

The unit of current is in amperes (A).

Calculation:

Differentiate the equation (1) as below.

Q'(t)=3t24t+6

Calculate the current when t is 0.5s.

Substitute the value of 0.5s for t in above Q'(t) equation.

Q'(0.5)=3(0.5)24(0.5)+6Q'(0.5)=4.75A

Therefore, the magnitude of current when time t is equal to 0.5s is 4.75A_.

(b)

To determine

To find: The magnitude of current when the value of time is given as t=1s, also the time at which the lowest value of current occurs.

Expert Solution

Answer to Problem 19E

The current when time t is equal to 1s is 5A_.

The current is lowest at the time equal to 23sec_.

Explanation of Solution

Calculate the current when time t is equal to 1s.

Substitute the value 1s for t in above Q'(t) equation.

Q'(1)=3(1)24(1)+6Q'(1)=5A

Therefore, the current when t is equal to 1s is 5A_.

Calculate at what time the current is lowest.

The current is lowest when the Q' has a minimum value.

Differentiate Q' again,

Q"(t)=6t4

Equating the Q"(t) to zero.

Q"(t)=6t4=06t4=06t=4t=46t=23s

When the value of time t<23s, current is decreasing.

Substituting the value of 12s for t in Q''(t).

Q''(12)=6(12)4Q''(12)=1A<0

When the value of time t>23, current is increasing.

Substituting the value 1 for t in Q''(t).

Q''(1)=6(1)4Q''(1)=2A>0

Therefore, the current is lowest at the time 23sec.

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