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Chapter 31 Homework
Due: 8:00am on Thursday, March 25, 2010
Note: To understand how points are awarded, read your instructor's Grading Policy.
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Current in a Wire
A metallic wire has a diameter of
. When the current in the wire is
, the drift velocity is
.
Part A
What is the density of free electrons in the metal?
Hint A.1
How to approach the problem
Recall the definition of current as the net charge flowing through a given cross-sectional area per unit time. If you express the net charge flowing through the area in terms of the concentration of the charge carriers per
unit volume, you will find that the current depends on the concentration and charge of the charged particles, as well as on the magnitude of their drift velocity. Recall that in metals the charge carriers are free
electrons.
Hint A.2
Current as a function of concentration of the charge carriers
Consider a wire of cross-sectional area , with current . Let
particles). Then the current is given by
Express your answer numerically in
ANSWER:
, where
be the drift velocity of the free charges in the conductor and
the number of charged particles per unit volume (i.e., the concentration of charged
is the magnitude of the charge on a charge carrier.
to two significant figures.
6.95×1028
Correct
Problem 31.6
The electron drift speed is
in a metal with a mean free time between collisions of
.
Part A
What is the electric field strength?
ANSWER:
2.28×10−2 N/C
Correct
Problem 31.15
The current in an electric hair dryer is 10.0 A.
Part A
How much charge flows through the hair dryer in 5.0 min?
ANSWER:
3000
Correct
Part B
How many electrons flow through the hair dryer in 5.0 min?
ANSWER:
1.88×1022
Correct
Problem 31.22
−2
The electric field in a
square aluminum wire is 3.0×10
.
Part A
What is the current in the wire?
Express your answer using two significant figures.
ANSWER:
= 1.5
Correct
Problem 31.48
A car battery is rated at
, meaning that it can supply a 90 A current for 1 hr before being completely discharged.
Problem 31.53
Part A
The total amount of charge in coulombs that has entered a wire at time is given by the expression
, where is in seconds and
.
If you leave your headlights on until the battery is completely dead, how much charge leaves the battery? Express your answer in Coulombs to three significant figures.
Part A
ANSWER:
5
Graph versus for the3.24×10
interval C
Correct
.
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ANSWER:
View
Correct
Part B
Find an expression for the current in the wire at time .
ANSWER:
Correct
Part C
Graph
versus
for the interval
.
ANSWER:
View
Correct
Part D
Explain why
has the value at
ANSWER:
that you observe.
My Answer:
A Five Wire Junction
Learning Goal: To learn to apply the concept of current density and Kirchhoff's junction rule.
Consider a junction of five wires, as shown in the figure. The arrows indicate the direction of current flow.
The information about the magnitudes of the current density and the diameters for wires 1, 2, 3, and 4 is given in the table. Some of the values are unknown.
Current density (
Wire
)
Diameter (
Total Current ( )
)
1
1.6
2.0
???
2
???
3.0
2.0
3
3.0
1.1
???
4
0.8
???
4.0
Part A
Find the current
Hint A.1
in wire 5.
How to approach the problem
Hint not displayed
Hint A.2
Kirchhoff's rule
Hint not displayed
Hint A.3
Current density and current
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Hint not displayed
Hint A.4
Area of the wire
Hint not displayed
Express your answer in amperes. Use two significant figures. Assume that the current out of the junction is positive and that the current into the junction is negative.
ANSWER:
= -9.9
Correct
Note that you did not have to find all the unknown quantities in the table. Separating useful information from the useless (irrelevant) is an important skill that you are expected to develop in studying physics.
Score Summary:
Your score on this assignment is 98.2%.
You received 44.17 out of a possible total of 45 points.
3/24/2010 8:43 PM