Chapter 17: Current and Resistance

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Chapter 17 Current and Resistance

• Electric Current

Homework assignment 18, 38, 51, 60, 67

• Definition of electric current

A current is any motion of charge from one region
to another.

• Suppose a group of charges move perpendicular
• to surface of area A.

• The current is the rate that charge flows
  through
• this area

SI unit 1 A 1 ampere 1 C/s
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• Electric Current

• Example 17.1 Turn on the light

• The amount of charge that passes through the
  filament of a
• certain lightbulb in 2.00 s is 1.67 C. Find
• the current in the bulb and (b) the number of
  electrons that pass
• through the filament.

(a)
(b)
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• A Microscopic View of Current

• Microscopic view of current

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• A Microscopic View of Current

• Microscopic view of current (contd)

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• A Microscopic View of Current

• Microscopic view of current (contd)

• In time Dt the electrons move a distance

• There are n particles per unit volume that carry
  charge q

• The amount of charge that passes the area A in
  time Dt is

• The current I is defined by

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• A Microscopic View of Current

• Example 17.2 Drift speed of electrons

• A copper wire of cross-sectional area 3.00x10-6
  m2 caries a current
• of 10.0 A.
• Assuming that each copper atom contributes one
  free electron
• to the metal, find the drift speed of the
  electrons in this wire.

vol. of one mole of copper
(b) Using the ideal gas model to compare the
drift speed with the random rms speed an
electron would have at 20.0oC.
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• Current and Voltage Measurements in Circuits

• Circuit diagram

Battery
Ammeter measures the
current Voltmeter measures the
electric potential difference
-

Bulb
-

A
Ammeter
V
-

Voltmeter
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• Resistance and Ohms Law

• Resistance and Ohms law

• When a voltage (potential difference) DV is
  applied across
• the ends of a metallic conductor, the current
  in the conductor
• is found to be proportional to the applied
  voltage

Va
Ohms law
I
The proportionality constant is called
resistance. SI unit is ohm (W ) .
A
Vb
DVVb-Va
SI unit ohm (W) volt/amper (V/A)

• A resistor is a conductor that provides a
  special resistance in an
• electrical circuit Symbol

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• Resistance and Ohms Law

• Resistance and Ohms law (contd)

• For many materials, including most metals, the
  resistance remains
• constant over a wide range of applied voltages
  or currents.

• Materials that obey the Ohms law over a wide
  range of voltage
• are said to be ohmic. Otherwise they are said
  to be nonohmic.

I
I
DV
DV
semiconductor diode
resistor that obeys Ohms law
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• Resistivity

• Resistivity

• The resistance of an ohmic conductor increases
  with length l.

The electrons go through the conductor encounter
more collisions

• A smaller cross-sectional area A also increases
  the resistance of
• a conductor.

r resistivity l length A area
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• Temperature Variation of Resistance

• Resistivity and temperature

• The resistivity of a metallic conductor nearly
  always increases with
• increasing temperature.

reference temp. (often 0 oC)
temperature coefficient of resistivity
Material
a (oC)-1
Material
a (oC)-1
aluminum
iron
lead
brass
manganin
graphite
silver
copper
platinum
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• Temperature Variation of Resistance

• Example 17.5 A platinum resistance thermometer

• A resistance thermometer, which measures
  temperature by
• measuring the change in resistance of a
  conductor, is made of
• platinum and has a resistance of 50.0 W at
  20.0oC.
• (a) When the device is immersed in a vessel
  containing melting
• indium, its resistance increases to 76.8 W.
  From this information
• find the melting point of indium.

(b) The indium is heated further until it reaches
a temperature of 235oC. What is the ratio
of the new current in the platinum to the
current Imp at the melting point?
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• Superconductors

• Resistivity vs. temperature and superconductor

• The resistivity of graphite decreases with the
  temperature, since at higher
• temperature more electrons become loose out of
  the atoms and more mobile.

• This behavior of graphite above is also true for
  semiconductors.

• Some materials, including several metallic
  alloys and oxides, has a property
• called superconductivity. Superconductivity is
  a phenomenon where the
• resistivity at first decreases smoothly as the
  temperature decreases, and then
• at a certain critical temperature Tc the
  resistivity suddenly drops to zero.

r
r
r
T
T
T
Tc
semiconductor
superconductor
metal
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• Electrical Energy and Power

• Electrical energy and power

• A battery is used to establish an electric
  current in a conductor by
• converting chemical energy stored in the
  battery into kinetic energy
• of the charged carriers such as electrons.

• The kinetic energy of the carriers is lost as a
  result of collisions
• between the charge carriers and fixed atoms in
  the conductor
• (resistance).

Point A reference point VA0
(grounded)

• Imagine the charge moves from A to B to
• C to D to A.

A-B Energy increases by
B-C No change in energy
B
C
C-D Energy decreases by
A
D
Energy lost in Dt
Power lost to resistor
ground
SI unit watt (W)
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• Electrical Energy and Power

• Example 17.7 The power converted by an
  electric heater

• An electric heater is operated by applying a
  potential difference
• of 50.0 V to a nichrome wire of total
  resistance 8.00 W.
• (a) Find the current carried by the wire and
  the power rating of the
• heater.

(b) Using this heater, how long would it take to
heat 2.50x103 moles of diatomic gas (e.g. a
mixture of oxygen and nitrogen-air) from
10.0oC to 25.0oC? Take the molar specific heat at
constant volume of air to be (5/2)R.
D UQW and W0
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• Electrical Activity in the Heart

• Heart and electrocardiograph

• Every action involving the bodys muscles is
  initiated by electrical
• activity.

• The voltage produced by muscular action in the
  heart are particularly
• important to physicians. Voltage pulses cause
  heart to beat, and the
• waves of electrical excitation that sweep
  across the heart associated
• with the heartbeat are conducted through the
  body via the body fluids.

• These voltage pulses can be
• detected by an equipment
• attached to the skin.

Sinoartrial (SA) node
LA

• This equipment electro-
• cardiograph is basically
• made of a voltmeter that
• measures pulses in 1 mV
• range.

RA
LV
Atrioventricular (AV) node
RL

• The pattern recorded by this
• device is called electro-
• cardiogram.

RA right atrium, LA left atrium, RV right
ventricle, LV left ventricle
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• Electrical Activity in the Heart

• Heart activity and EKG

• As the SA node fires, each electrical impulse
  travels through the
• right and left atrium.

• This electrical activity causes the two
• upper chambers to contract. This activity
• is recorded as P-wave on EKG.

• The electrical impulse then moves to an
• known as the AV node just above the
• ventricles. Here the electrical impulse
• is held up for a brief period. This delay
• allows the right and left atrium to empty
• the blood into the two ventricles. This
• delay is recorded as PR interval on EKG.

• After the delay, the impulse travels
• through both ventricles and cause them to
  contract, and the blood
• is emptied into the pulmonary artery and aorta.
  This activity is
• recorded as QRS-complex on EKG.

• Then ventricles recover from its electrical
  stimulation and generate
• an ST-segment and T waves on EKG.