Chapter 28 Current and Resistance

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Chapter 28 Current and Resistance

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Moving charges
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Electric current
The current is the rate at which charge flows
through this surface.
The direction of the current is defined to be the
direction of the positive charge flow. However,
in metals, electrons flow in the opposite
direction of the current.
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Definition and unit of current
The unit of current is called the ampere (A)
Current is a scalar, even though we often use an
arrow to indicate the current flow directions in
wires.
i1
i0
i2
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Sample problem 1
Water flows through a garden hose at a volume
flow rate of 450 cm3/s. What is the current of
negative charge?
Ans 2.42 ? 107 A 24.1 MA
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Current density
If the current density is uniform
If the current density is also normal to the
surface
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Drift speed
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Sample problem 2

1. The current density in a cylindrical wire of
   radius R 2.0 mm is uniform across a cross
   section of the wire and is J 2.0 ? 105 A/m2.
   What is the current through the outer portion of
   the wire between radial distances R/2 and R?
2. Suppose, instead, that the current density
   through a cross section varies with radial
   distance r as J ar2, in which a 3.0 ? 1011
   A/m4 and r is in meter. What is the current
   through the same outer portion of the wire?

(a) 1.9 A (b) 7.1 A.
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Sample problem 3
What is the drift speed of the conduction
electrons in a copper wire with radius r 900 ?m
when it has a uniform current i 17 mA? Assume
that each copper atom contributes one conduction
electron to the current and the current density
is uniform across the wires cross section.
Ans. vd 4.9 ? 10-7 m/s.
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Resistance
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Ohms law
or
Georg Simon Ohm (1789-1854)
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I-V curves Ohms law
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Color coding for resistors
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Variation with temperature
where T0 is a selected reference temperature and
?0 is the resistivity at that temperature.
Usually T0 293 K, for which ?0 1.69 ? 10-8
?m for copper.
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Sample problem 4
A rectangular block of iron has dimensions 1.2 cm
? 1.2 cm ? 15 cm. A potential difference is to be
applied to the block between parallel sides and
in such a way that those sides are equipotential
surfaces. What is the resistance of the block if
the two parallel sides are (1) the square ends,
and (2) two rectangular sides.
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A microscopic view
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A microscopic view of Ohms law
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Sample problem 5
(a) What is the mean free time ? between
collisions for the conduction electrons in
copper? (b) What is the mean free path ? between
collisions for the conduction electrons in
copper, assuming that their effective speed veff
is 1.6 ? 106 m/s?
(a)
(b)
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Power in electric circuits
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Sample problem 6
A length of heating wire, made of
nickel-chromium-iron alloy called Nichrome, has a
resistance R of 72 ?. At what rate is the energy
dissipated in each of the following cases? (1) A
potential difference of 120 V is applied across
the full length of the wire. (2) The wire is cut
in half, and a potential difference of 120 V is
applied across the length of each half.
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semiconductors
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superconductors
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Levitation with superconductors
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Home work
Question (??) 12, 15, 16
Exercise (???) 5, 11, 15
Problem (??) 14, 38, 40, 42