Assignment 10: Current and Resistance

Due: 8:00am on Friday, February 10, 2012

Note: To understand how points are awarded, read your instructor's Grading Policy.

Current in an Ionic Solution

Current passes through a solution of sodium chloride. In 1.00 second, ions arrive at the negative

electrode and ions arrive at the positive electrode.

Part A

What is the current passing between the electrodes?

Hint A.1 General considerations on ionic solutions

Hint not displayed

Hint A.2 Find the current due to the positive ions

Hint not displayed

Express your answer in milliamperes to three significant figures.

ANSWER:

10.6

Correct

Part B

What is the direction of the current in the ionic solution?

Hint B.1 Conventional direction of current

Hint not displayed

ANSWER:

away from the negative electrode

toward the negative electrode

Correct

A Stretchable Resistor

A wire of length and cross-sectional area has resistance .

Part A

What will be the resistance of the wire if it is stretched to twice its original length? Assume that the density

and resistivity of the material do not change when the wire is stretched.

Hint A.1 Formula for the resistance of a wire

Hint not displayed

Hint A.2 Find the cross-sectional area of the stretched wire

Hint not displayed

Express your answer in terms of the wire's original resistance .

ANSWER: =

Correct

± Jumper Cables and Ohm's Law

Learning Goal: To learn to apply the concept of current density and microscopic Ohm's law.

A "gauge 8" jumper cable has a diameter of 0.326 centimeters. The cable carries a current of 30.0 amperes. The

electric field in the cable is 0.062 newtons per coulomb.

Part A

What is the material of the cable?

Hint A.1 How to approach the problem

Hint not displayed

Hint A.2 Find the resistivity

Hint not displayed

Hint A.3 Resistivity of common metals

Hint not displayed

Choose the correct metal that makes up the cable.

ANSWER:

copper

silver

aluminum

gold

steel

Correct

Part B

What electric field would have been required to create a current of 30.0 amperes in an aluminum wire of the

same diameter? The resistivity of aluminum is ohm-meters.

Hint B.1 How to approach the problem

Hint not displayed

Hint B.2 Resistivity defined

Hint not displayed

Express your answer in newtons per coulomb. Use three significant figures.

ANSWER:

=

9.90×10−2

Correct

Part C

What electric field would have been required to create a current of 30.0 amperes in a copper "gauge 10" wire

with diameter equal to 0.259 centimeters?

Express your answer in newtons per coulumb. Use three significant figures.

ANSWER:

=

9.80×10−2

Correct

Part D

The resistance of a copper "gauge 10" jumper cable with diameter centimeters is 0.0124 ohms. Find the

length of the cable.

Hint D.1 Resistance defined

Hint not displayed

Express your answer in meters. Use three significant figures.

ANSWER:

=

3.80

Correct

Exercise 25.12

A copper wire has a square cross section 2.5 on a side. The wire is 4.4 long and carries a current of 3.9 .

The density of free electrons is .

Part A

Find the magnitude of the current density in the wire.

Express your answer using two significant figures.

ANSWER:

=

6.2×105

Correct

Part B

Find the magnitude of the electric field in the wire.

Express your answer using two significant figures.

ANSWER:

=

1.1×10−2

Correct

Part C

How much time is required for an electron to travel the length of the wire?

Express your answer using two significant figures.

ANSWER:

=

9.6×104

Correct

Maximum Current and Current Density in a Cuboidal Resistor

A rectangular block of metal of resistivity has dimensions . A potential difference is to be applied

between two opposite faces of the block.

Part A

To which two faces of the block should the potential difference be applied to give the maximum current density?

Hint A.1 Calculate the current density in a rectangular block of metal

Hint not displayed

ANSWER:

to the faces that are a distance apart

to the faces that are a distance apart

to the faces that are a distance apart

Correct

Part B

What is the maximum current density from Part A?

Hint B.1 How to approach the problem

Hint not displayed

Express your answer in terms of some or all of the variables , (the resistivity of the material), and .

ANSWER:

=

Correct

Part C

To which two faces of the block should the potential difference be applied to give the maximum current?

Hint C.1 Calculate the current in a rectangular block of metal

Hint not displayed

ANSWER:

to the faces that are a distance apart

to the faces that are a distance apart

to the faces that are a distance apart

Correct

Part D

What is this maximum current?

Hint D.1 How to approach the problem

Hint not displayed

Express your answer in terms of some or all of the variables , (the resistivity of the material), and .

ANSWER:

=

Correct

Stretching the A-Rod

Learning Goal: To learn to apply the concept of current density and microscopic Ohm's law.

A slab of metal of volume is made into a rod of length . The rod carries current when the electric field inside is

.

Part A

Find the resistivity of the metal .

Hint A.1 How to approach the problem

Hint not displayed

Hint A.2 Definition of resistivity

Hint not displayed

Hint A.3 Find the current density

Hint not displayed

Expess your answer in terms of the given quantities.

ANSWER:

Correct

Part B

The rod is now stretched so that its length is doubled. If the electric field remains the same, what is the new

current in the rod?

Hint B.1 How to approach the problem

Hint not displayed

Express your answer in terms of some or all of the quantities given in the problem introduction.

ANSWER:

=

Correct

Part C

A piece of copper is made into a rod with a square cross-section. The side of the square is 2.00 centimeters. The

resistivity of copper is . An unknown electric field , directed along the rod, creates a current of 12.0

amperes through the rod. Find the magnitude of .

Hint C.1 How to approach the problem

Hint not displayed

Hint C.2 Definition of resistivity

Hint not displayed

Use two significant figures in your answer. Express your answer in newtons per coulomb.

ANSWER:

=

5.10×10−4

Correct

Problem 25.58

A 2.0- length of wire is made by welding the end of a 120- -long silver wire to the end of an 80- -long copper

wire. Each piece of wire is 0.60 in diameter. The wire is at room temperature. A potential difference of 5.0 is

maintained between the ends of the 2.0- composite wire.

Part A

What is the current in the copper section?

Express your answer using two significant figures.

ANSWER:

=

45

Correct

Part B

What is the current in the silver section?

Express your answer using two significant figures.

ANSWER:

=

45

Correct

Part C

What is the magnitude of in the copper?

Express your answer using two significant figures.

ANSWER:

=

2.8

Correct

Part D

What is the magnitude of in the silver?

Express your answer using two significant figures.

ANSWER:

=

2.3

Correct

Part E

What is the potential difference between the ends of the silver section of wire?

Express your answer using two significant figures.

ANSWER:

=

2.8

Correct

Problem 25.66

The region between two concentric conducting spheres with radii and is filled with a conducting material with

resistivity .

Part A

Find the resistance between the spheres.

Express your answer in terms of the variables , , and appropriate constants.

ANSWER:

=

Correct

Part B

Derive an expression for the current density as a function of radius, in terms of the potential difference

between the spheres.

Express your answer in terms of the variables , , , , and appropriate constants.

ANSWER:

=

Correct

Part C

Show that the result in part (a) reduces to the equation when the separation between the spheres is

small.

Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

ANSWER: My Answer: