Chapters 25Examples

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Chapters 25--Examples
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Problem

• The current in a wire varies with time according
  to the relation
• I55A-(0.65 A/s2)t2
• How many coulombs of charge pass through a
  cross-section of wire in the time interval from
  t0 s to t8 s?
• What constant current would transport the same
  amount of charge?

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Integratin means summin

• Need to sum the charge between t0 to t8 i.e.
  integrate

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Problem

• A current-carrying gold wire has a diameter of
  0.84 mm. The electric field is 0.49 V/m . What
  is
• The current carried by the wire?
• The potential difference between two points 6.4 m
  apart?
• The resistance of a 6.4 m length of this wire?

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Part A
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Part B
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Part C
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Problem

• A beam contains 2 x 108 doubly charged positive
  ions per cubic centimeter, all of which are
  moving north with a speed of 1x105 m/s.
• What is the magnitude and direction of the
  current density J?
• Can you calculate the total current i in the
  beam? If not, what else do you need to know?

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Part A

• Jnqvd
• n 2 x 108 ions/cc and 1 cc 1/1003 m3 so n 2x
  1014 ions/m3
• q2e 2 1.602x10-19
• vd 105 m/s
• J(2x1014)(21.602x10-19)105
• J6.4 A/m2 and J is in same direction as vd

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Part B

• iJA but what is A?

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Problem

• A pn junction is formed from two different
  semiconducting materials in the form of identical
  cylinders with a radius of 0.165 mm (as shown
  below). In one application, 3.5 x 1015
  electrons/second flow from the n side to the p
  side while 2.25 x 1015 holes (positive charge
  carriers) flow from the p to the n side. What
  is a) the total current and b) the charge density?

n
p
p
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Part A

• Find net charge(nenh)e
• (3.5 x 1015 2.25 x 1015)1.602 x 10-19
• Both of these were charge rates (rates/second)
• So i (3.5 x 1015 2.25 x 1015)1.602 x 10-19
  9.2 x 10-4 A

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Part B

• Ji/A
• Apr2
• where r0.165 mm 0.165 x 10-3 m
• J(9.2 x 10-4)/(p (0.165 x 10-3 )2
• J1.08 x 104 A/m2

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Problem

• How long does it take electrons to get from a car
  battery to the starting motor? Assume the
  current is 300 A and the electrons travel through
  a copper wire with cross-sectional area 0.21 cm2
  and length 0.85 m?

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Prep Stuff

• r for Cu 1.69 x 10-8 Wm
• A0.21 cm2 where 1 cm2 (1/100)2 m2
• nnumber of electrons/ m3
• Assume 1 conduction electron for each Cu atom
• Mass/m3 (mol/mass)(atoms/mol)atoms/m3
• The atomic weight is the mass/mol 64 x 10-3
  kg/m3
• The number of atoms per mol is Avogadros number
  (6.02 x 1023)
• Density of Cu 9000 kg/m3
• n9000(1/64)6.02 x 10238.47 x 1028 atoms/m3 or
  e/m3

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Solution

• Jnqvd
• vd J/(nq) where Ji/A
• vd i/(nqA)
• dvt or td/vd
• td(nqA)/(i)
• t(0.85)(8.47 x 10281.602x 10-19 0.21x104)/300
• t8.1 x 102 s13 min