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CHAPTER 27
ELECTRIC CURRENT
Section 27

1:
Electric Current
Problem
1.
A wire carries 15
. A. How many electrons pass through the wire in each second?
Solution
The current is the amount of charge passing a given point in the wire, per unit time, so in one second,
∆∆
q
I
t
==
=
A
s
C
.
(.
)
( )
.
15
1
The number of electrons in this amount of charge is 15
16 10
938 10
19
18
..
.
.
C
C
=
×=
×
−
Problem
2.
In an ionic solution, 41 10
15
.
×
ions, each carrying charge
+
2
e
, pass to the right each second, 36 10
15
.
×
ions, each
carrying
−
e
, pass to the left in the same time. What is the net current?
Solution
The net current (taken as positive to the right) is
)
( ) (.
)
)
41 10
2
36 10
1
15
1
15
1
19
×+
×
−
−
=
×
×
−
−
s
s
C
ee
.
)
.
24
13
6 1
0
1
8
9
15
1
×
=
−
m
A
.
(The factor
−
1 in the negative ion current represents a drift velocity to the left.)
Problem
3.
A 12V car battery is rated at 80 amperehours, meaning it can supply 80 A of current for 1 hour before it becomes
discharged. If you accidentally leave the headlights on until the battery discharges, how much charge moves through the
lights?
Solution
A battery rated at 80 A h
⋅
can supply a net charge of
qI
t
=×
C/s
s
C
()
.
.
80
3600
2 88
10
5
Problem
4.
The electron beam that “paints” the image on a computer screen contains 50 10
6
.
×
electrons per cm of its length. If the
electrons move toward the screen at 60 10
7
.
×
m/s, how much current does the beam carry? What is the direction of this
current?
Solution
In Equation 272,
nA
is the number of charge carriers per unit length of beam, so
In
A
q
d
×
×
−
v
51
0
61
cm
)
(
)
.
16
10
6
48
19
7
××
=
−
m
/
s
m
A
.
This is the magnitude of the current; since electrons are negatively charged, the
direction of the current is opposite to the drift velocity.
Problem
5.
Microbiologists measure total current due to potassium ions
K
+
moving through a cell membrane of a rock crab
neuron cell to be 30 nA. How many ions pass through the membrane each second?
Solution
The charge moving through the membrane each second is 30 nC. Since singlycharged ions carry one elementary charge
(about 160 zC), this corresponds to 30
160
188
10
6 02
10
11
23
nC
zC/ion
ion
ion/mol)
0.311 pmol.
(
.
)
(
.
×
=
(See
Example 272(a), Appendix B, and Table 11.) Chemical drugtesting instrumentation can detect amounts of substances
this low.
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View Full DocumentCHAPTER 27
643
Problem
6.
An ion channel in a cell membrane carries 2.4 pA when it’s open, but it’s only open 20% of the time. (a) What is the
average current in the channel? (b) If the channel opens for 10
.m
s
, how many singly ionized ions pass through it in this
time?
Solution
(a) The average current is a timeweighted average over subintervals
(,)
,
∆
∆
∆
∆
∆∆
qt
It t
t
t
I
ii
i
==
= ∑
∑=
=
where
so
av
(.
4
)
()
.
4
8
20%)(2
80%)(0
0
pA
pA.
+=
(b) The number of singlycharged ions passing through the channel while current is
flowing is
qe
I te
=
=
×
pA
ms
zC
4
)
)(
)
.
2
10
160
15
10
4
(see solution to previous problem).
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 Spring '08
 Dougherty

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