Chapter 26. Current and Resistance

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Chapter 26. Current and Resistance

• 26.1. What is Physics?      
• 26.2. Electric Current      
• 26.3. Current Density      
• 26.4. Resistance and Resistivity      
• 26.5. Ohm's Law      
• 26.6. A Microscopic View of Ohm's Law      
• 26.7. Power in Electric Circuits      
• 26.8. Semiconductors      
• 26.9. Superconductors

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What is Physics?  
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Electric Current

• The electric current is the amount of charge per
  unit time that passes through a plane that pass
  completely through the conductor.

The SI unit for current is a coulomb per second
(C/s), called as an ampere (A)
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Current is a Scalar
                                                                                             

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Direction of current

• A current arrow is drawn in the direction in
  which positive charge carriers would move, even
  if the actual charge carriers are negative and
  move in the opposite direction.
• The direction of conventional current is always
  from a point of higher potential toward a point
  of lower potentialthat is, from the positive
  toward the negative terminal.

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Current Density

• Current density is to study the flow of charge
  through a cross section of the conductor at a
  particular point
• It is a vector which has the same direction as
  the velocity of the moving charges if they are
  positive and the opposite direction if they are
  negative.
• The magnitude of J is equal to the current per
  unit area through that area element.

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Drift Speed

                                                                                              

• When a conductor does not have a current
  through it, its conduction electrons move
  randomly, with no net motion in any direction.
  When the conductor does have a current through
  it, these electrons actually still move randomly,
  but now they tend to drift with a drift speed vd
  in the direction opposite that of the applied
  electric field that causes the current

    
Here the product ne, whose SI unit is the coulomb
per cubic meter (C/m3), is the carrier charge
density
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Sample Problem 26-3

• What is the drift speed of the conduction
  electrons in a copper wire with radius r900 µm
  when it has a uniform current i17 mA? Assume
  that each copper atom contributes one conduction
  electron to the current and that the current
  density is uniform across the wire's cross
  section. Mass density of copper is ?8.96x103
  kg/m3 .

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The resistance
                                                                                                                                                            

• The resistance (R) is defined as the ratio of the
  voltage V applied across a piece of material to
  the current I through the material RV/i.
• SI Unit of Resistance volt/ampere (V/A)ohm(O)

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The resistance of a conductor depends on the
manner in which the potential difference is
applied to it
                                                                                                 

Ra gt Rb
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Resistivity
Resistivity of a material is
 The unit of ? is ohm-meter (Om)                                                                     

The conductivity s   of a material is
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Resistivity

• The resistivity is an inherent property of the
  material
• The resistivity of a material depends on
  temperature. ? ? 01 a(T - T0)
• The term a has the unit of reciprocal
  temperature and is the temperature coefficient of
  resistivity.

                                                                                                             

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 2.82

 3.5

 1.72

 2.44

 9.7

 95.8

 100

 1.59

 5.6

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Table 20.1   Resistivitiesa of Various Materials


 Material   Resistivity r (Wm)   Material   Resistivity r (Wm) 

 Conductors      Semiconductors    
   Aluminum  108     Carbon  105 
   Copper  108     Germanium   0.5bc  
   Gold  108     Silicon   202300bc  
   Iron  108   Insulators 
   Mercury  108     Mica   10111015 
   Nichrome (alloy)  108     Rubber (hard)   10131016 
   Silver  108     Teflon   1016 
   Tungsten  108     Wood (maple)  1010 

aThe values pertain to temperatures near 20 C. aThe values pertain to temperatures near 20 C. aThe values pertain to temperatures near 20 C. aThe values pertain to temperatures near 20 C.
bDepending on purity. bDepending on purity. bDepending on purity. bDepending on purity.
cDepending on purity. cDepending on purity. cDepending on purity. cDepending on purity.
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Calculating Resistance from Resistivity

                                                                                                

• Resistance is a property of an object. It may
  vary depending on the geometry of the material.
• Resistivity is a property of a material.

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Checkpoint

• The figure here shows three cylindrical copper
  conductors along with their face areas and
  lengths. Rank them according to the current
  through them, greatest first, when the same
  potential difference V is placed across their
  lengths.

    

                                                                                                                                                     

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Sample Problem


                                                                                                 

• A rectangular block of iron has dimensions
  1.2cmx1.2cmx15cm . A potential difference is to
  be applied to the block between parallel sides
  and in such a way that those sides are
  equipotential surfaces (as in Fig. b). What is
  the resistance of the block if the two parallel
  sides are (1) the square ends (with dimensions )
  1.2cmx1.2cm and (2) two rectangular sides (with
  dimensions 1.2cmx15cm )?

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Sample Problem 26-5

• Figure 26-11 shows a person and a cow, each a
  radial distance D60m from the point where
  lightning of current i10kA strikes the ground.
  The current spreads through the ground uniformly
  over a hemisphere centered on the strike point.
  The person's feet are separated by radial
  distance ?rper0.50m the cow's front and rear
  hooves are separated by radial distance
  ?rcow1.50m. The resistivity of the ground is
  ?gr100 Om . The resistance both across the
  person, between left and right feet, and across
  the cow, between front and rear hooves, is
  R4.00kO. (a) What is the current ip through the
  person? (b) What is the current ic through the
  cow?

                                                                                                                                                         

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Example

• Two conductors are made of the same material
  and have the same length. Conductor A is a solid
  wire of diameter 1.0 mm. Conductor B is a hollow
  tube of outside diameter 2.0 mm and inside
  diameter 1.0 mm. What is the resistance ratio
  RA/RB, measured between their ends?

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Ohm's Law

• Ohm's law is an assertion that the current
  through a device is always directly proportional
  to the potential difference applied to the device.

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Ohmic Material

• The ohmic material type of materials (e.g.,
  metals) which obeys Ohm's law.
• The non-ohmic material type of materials which
  does not obey Ohm's law.
• A conducting device obeys Ohm's law when the
  resistance of the device is independent of the
  magnitude and polarity of the applied potential
  difference.
• A conducting material obeys Ohm's law when the
  resistivity of the material is independent of the
  magnitude and direction of the applied electric
  field.

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Power in Electric Circuits

• The amount of charge dq that moves from terminals
  a to b in time interval dt is equal to i dt.
• Its electric potential energy decreases in
  magnitude by the amount

• The decrease in electric potential energy from a
  to b is accompanied by a transfer of energy to
  some other form. The power P associated with that
  transfer is the rate of transfer
• d U/dt, which is

                                                                              

• The unit of power

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the transfer of electric potential energy to
thermal energy
                                                                                            (26-27)


                                                                                                                   
The rate of electrical energy dissipation due to
a resistance is

• Caution
• PiV applies to electrical energy transfers of
  all kinds        
• Pi2R and PV2/R apply only to the transfer of
  electric potential energy to thermal energy in a
  device with resistance.

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Sample Problem

• You are given a length of uniform heating wire
  made of a nickelchromiumiron alloy called
  Nichrome it has a resistance R of 72 O. At what
  rate is energy dissipated in each of the
  following situations? (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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Sample Problem

• A copper wire of cross-sectional area
  and length 4.00 m has a current of
  2.00 A uniformly distributed across that area.
  (a) What is the magnitude of the electric field
  along the wire? (b) How much electrical energy is
  transferred to thermal energy in 30 min?

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Semiconductors
Property Copper Silicon
Type of material Metal Semiconductor
Charge carrier density, m-3
Resistivity,        
Temperature coefficient of resistivity, K-1




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 Superconductors
The resistivity of material absolutely disappears
at very low temperatures. This phenomenon of
superconductivity

                                                                                              
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Conceptual Questions

1. When an incandescent light bulb is turned on, the
   tungsten filament becomes white hot. The
   temperature coefficient of resistivity for
   tungsten is a positive number. What happens to
   the power delivered to the bulb as the filament
   heats up? Does the power increase, remain the
   same, or decrease? Justify your answer.
2. Two materials have different resistivities. Two
   wires of the same length are made, one from each
   of the materials. Is it possible for each wire to
   have the same resistance? Explain.
3. One electrical appliance operates with a voltage
   of 120 V, while another operates with 240 V.
   Based on this information alone, is it correct to
   say that the second appliance uses more power
   than the first? Give your reasoning.

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1. Two light bulbs are designed for use at 120 V and
   are rated at 75 W and 150 W. Which light bulb has
   the greater filament resistance? Why?
2. Often, the instructions for an electrical
   appliance do not state how many watts of power
   the appliance uses. Instead, a statement such as
   10 A, 120 V is given. Explain why this
   statement is equivalent to telling you the power
   consumption.