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Chapter 27: Q. 58 (page 764)

The total amount of charge in coulombs that has entered a wire at time tis given by the expression localid="1648639892228" Q=4t-t2, where tis in seconds andt鈮�0.
a. Find an expression for the current in the wire at timet.
b. Graph Iversus tfor the interval 0鈮�t鈮�4s.

Short Answer

Expert verified

(a) An expression for the current in the wire at time is 4-2t.

(b) Graph the interval 0鈮�t鈮�4sis,

Step by step solution

01

Given information Part (a)

The total amount of charge in a wire at time is tand is given by the expression Q=4t-t2, where t is in seconds.

02

Explanation Part (a)

The current is the amount of charge that departs per unit time. According to the infinitesimal definition, the current will be the time derivative of the expression of the charge. So, the current is

I=dQdt

=ddt4t鈭�t2

=4鈭�2t

Therefore, an expression for the current in the wire at time is4-2t

03

Given information Part (b)

Graph the interval 0鈮�t鈮�4sfor Iversus t, will show the ensuing linear relation.

04

Explanation Part (b)

Conspiring this process with a graph will show the ensuing linear relation.

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