17'5 Resistivity

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17.5 Resistivity

• Expected R?L/A 
• The resistance of an ohmic conductor is
  proportional to its length, L, and inversely
  proportional to its cross-sectional area, A
• ? (rho) in ?m is the constant of
  proportionality and is called the resistivity of
  the material

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Example

• Determine the required length of nichrome
  (?10-6 Wm) with a radius of 0.65 mm in order to
  obtain R2.0 W.
• R?L/A?LRA/?

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• The resistivity depends on the material and the
  temperature

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17.6 Temperature Variation of Resistivity

• For most metals, resistivity increases with
  increasing temperature
• With a higher temperature, the metals
  constituent atoms vibrate with increasing
  amplitude
• The electrons find it more difficult to pass the
  atoms (more scattering!)

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Temperature Variation of Resistivity, cont

• For most metals, resistivity increases
  approximately linearly with temperature over a
  limited temperature range
• ?o is the resistivity at some reference
  temperature To
• To is usually taken to be 20 C
• ? is the temperature coefficient of resistivity
  unit 1/(?C)

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Temperature Variation of Resistance

• Since the resistance of a conductor with uniform
  cross sectional area is proportional to the
  resistivity, the temperature variation of
  resistance can be written

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Example

• The material of the wire has a resistivity of
  ?06.8?10-5 ?m at T0320?C, a temperature
  coefficient of ?2.0?10-3 (1/?C) and L1.1 m.
  Determine the resistance of the heater wire at an
  operating temperature of 420?C.

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Solution

• ??01?(T-T0)
• ?6.8?10-5 ?m1(2.0?10-3 (?C)-1) ?
• ?(420?C-320?C)8.2?10-5 ?m
• R?L/A
• R(8.2?10-5 ?m)(1.1 m)/(3.1?10-6 m2)
• R29 ?

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17.7 Superconductors
normal

• A class of materials and compounds whose
  resistances fall to virtually zero below a
  certain temperature, TC
• TC is called the critical temperature (in the
  graph 4.1 K)

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Superconductors, cont

• The value of TC is sensitive to
• Chemical composition
• Pressure
• Crystalline structure
• Once a current is set up in a superconductor, it
  persists without any applied voltage
• Since R 0

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Superconductor Timeline

• 1911
• Superconductivity discovered by H. Kamerlingh
  Onnes
• 1986
• High-temperature superconductivity discovered by
  Bednorz and Müller
• Superconductivity near 30 K
• 1987
• Superconductivity at 92 K and 105 K
• Current
• More materials and more applications

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• Tc values for different materials note the high
  Tc values for the oxides.

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• Its magic!

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17.8 Electrical Energy and Power

• In a circuit, as a charge moves through the
  battery, the electrical potential energy of the
  system is increased by ?Q?V AsVWsJ
• The chemical potential energy of the battery
  decreases by the same amount
• As the charge moves through a resistor, it loses
  this potential energy during collisions with
  atoms in the resistor
• The temperature of the resistor will increase

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Electrical Energy and Power, cont
The rate of the energy transfer is power (P)
V
Units (C/s)(J/C) J/sW 1J1Ws1Nm WAV
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Electrical Energy and Power, cont

• From Ohms Law, alternate forms of power are (use
  VIR and IV/R)

Joule heat (I2R losses)
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Electrical Energy and Power, final

• The SI unit of power is Watt (W)
• I must be in Amperes, R in Ohms and V in Volts
• The unit of energy used by electric companies is
  the kilowatt-hour
• This is defined in terms of the unit of power and
  the amount of time it is supplied
• 1 kWh (103 W)(3600 s) 3.60 x 106 J

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17.9 Electrical Activity in the Heart
Heart beat Initiation

• Every action involving the bodys muscles is
  initiated by electrical activity
• Voltage pulses cause the heart to beat
• These voltage pulses (?1 mV) are large enough to
  be detected by equipment attached to the skin

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Electrocardiogram (EKG)

• A normal EKG
• P occurs just before the atria begin to contract
• The QRS pulse occurs in the ventricles just
  before they contract
• The T pulse occurs when the cells in the
  ventricles begin to recover

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Abnormal EKG, 1

• The QRS portion is wider than normal
• This indicates the possibility of an enlarged
  heart

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Abnormal EKG, 2

• There is no constant relationship between P and
  QRS pulse
• This suggests a blockage in the electrical
  conduction path between the SA and the AV nodes
• This leads to inefficient heart pumping

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Abnormal EKG, 3

• No P pulse and an irregular spacing between the
  QRS pulses
• Symptomatic of irregular atrial contraction,
  called fibrillation
• The atrial and ventricular contraction are
  irregular

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Implanted Cardioverter Defibrillator (ICD)
Dual chamber ICD

• Devices that can monitor, record and logically
  process heart signals
• Then supply different corrective signals to
  hearts that are not beating correctly

Monitor lead