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Chapter 27: Q. 5 (page 761)

What is the difference between current and current density?

Short Answer

Expert verified

Charge moves through a wire at a rate known as current.

The density of current flow within the conductors is called current density $J = \frac{I}{A} .$

Step by step solution

01

Concept Introduction

A conductor's current is defined as the rate at which electric charges flow through it. Current density is defined as the volumetric flow of charge per unit area through a conductor.

02

Explanation (Part a)

Difference between current and current density:

The current flow is sustained by an established electric field.

$I = \frac{q}{t}$

Here, $I$ is current in Ampere, $q$ is charge in Coulomb, and $t$ is time in seconds.

The current density written as follows.

$J = \frac{I}{A}$

Here, $J$ is current density in $A / m^{2}, I$ is current in Amperes, and $A$ is area of conductor in $m^{2} .$

03

Final Answer

Hence, In conductors, the current density can be defined as the density of current flow within the conductors. A stable current means that its magnitude and direction will always remain the same.

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Most popular questions from this chapter

The current in a $100 w a t t$ lightbulb is $0.85 A$ . The filament inside the bulb is $0.25 mm$ in diameter.

a. What is the current density in the filament?

b. What is the electron current in the filament?

The resistivity of a metal increases slightly with increased temperature. This can be expressed as $蚁 = 蚁_{0} [1 + 伪 (T - T_{0})]$ , where T0 is a reference temperature, usually 20掳C, and a is the temperature coefficient of resistivity.

a. First find an expression for the current I through a wire of length L, cross-section area A, and temperature T when connected across the terminals of an ideal battery with terminal voltage 鈭哣. Then, because the change in resistance is small, use the binomial approximation to simplify your expression. Your final expression should have the temperature coefficient a in the numerator.

b. For copper, a = 3.9 * 10-3 掳C-1 . Suppose a 2.5-m-long, 0.40-mm-diameter copper wire is connected across the terminals of a 1.5 V ideal battery. What is the current in the wire at 20掳C?

c. What is the rate, in A/掳C, at which the current changes with temperature as the wire heats up?

26. Wires $1$ and $2$ are made of the same metal. Wire $2$ has twice the length and twice the diameter of wire $1$ . What are the ratios (a) $蚁_{2} / 蚁_{1}$ of the resistivities and (b) $R_{2} / R_{1}$ of the resistances of the two wires?

20. What electric field strength is needed to create a $5.0 A$ current in a $2.0$ -mm-diameter iron wire?

FIGURE P27.42 shows a $4.0 c m$ wide plastic film being wrapped onto a $2.0 c m$ diameter roller that turns at $90 r p m .$ The plastic has a uniform surface charge density of $鈭� 2.0 nC / {cm}^{2}$ .

a. What is the current of the moving film?

b. How long does it take the roller to accumulate a charge of $- 10 渭 C ?$ ?

See all solutions

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