Current Electricity

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Current Electricity
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What You Will Learn

• Transfer of energy in circuits.
• Conversion of energy.
• Electric Current Conventional vs. Flow of
  Electrons
• Resistance and Ohms Law
• Basic Circuits

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What You Already Know

• You flip a switch to turn on a light, TV or
  computer.
• To turn on the car, you turn the ignition switch.
• MP3 players, cell phones and flashlights have
  on/off switches and use batteries.
• In each of these cases, you have a closed circuit
  in which electricity flows.

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What You Already Know

• Charge by Conduction The process by which
  electrons are transferred from one object to
  another because of differences in excess number
  of electrons on one surface compared to the other.

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What You Already Know - Electric Potential

• the Electric Potential Difference is equal to the
  Work required to move a test charge in an
  electric field divided by the magnitude of the
  test charge.

A
B
qo
F qoE
Uniform Electric Field
Vtotal W/qo Fd/qo Ed
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Creating a Circuit

What would happen if a was connected to both
plates?
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Creating a Circuit
The would flow from the charged
plate to the charged plate until the amount
of charge was the for both plates and the
wire.
How do we maintain the flow of ?
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Creating a Circuit

• Circuit
• A in which electric can flow.
• It generally includes a device such as a
  that reduces the .
• It also includes a device to increase potential
  energy ( ).

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What is Current?

• Current is the rate of flow of charge.
• I / 1 / 1 (
  )
• Conventional Current flow of . (Note
  that charges do flow in metallic
  conductors.)
• is simply
• the flow of .

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Ohms Law

• German Georg Simon Ohm discovered that the ratio
  of the potential difference to current is a
  constant for a given conductor.
• /___
• Where
• in ( )
• in ( )
• in ( )
• is the hindrance to the flow of .
• Most metallic conductors obey .

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Ohms Law

• The ( ) represents the ( ) of
  a curve where is plotted against .
• What is R?
• For materials, the curve is a straight line.

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Examples Ohms Law

• How much current flows through a 12? flashlight
  bulb operating at 3.0 volts?
• What is the voltage drop in a 5? resistor that
  has 2 amperes of current running through it?
• What is the resistance of a heating element in a
  toaster operating at 120 volts with a current
  flow of 2 amperes?

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What causes resistance?

• E-field in conductor (resistor) is provided by a
  battery or voltage source.
• Charges (electrons) are put in motion due to
  influences of the , but in a
  very short time from things that get in the way
• , ( ), etc
• The more , the greater the and the fewer
  the , the less the .
• Imagine the following two scenarios.
• Running down the hallway in between periods
• Running down the hallway after the late bell when
  there is nobody in them.
• Under which scenario would you experience less
  resistance?

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Resistivity Resistance

• Resistivity is a measure of the
  of the material.
• Resistivity is an intrinsic ( ) property of a
  material.
• The higher the , the higher the and vice
  versa.
• For a conductor of length L (m) and
  cross-sectional area A (m2), the resistance can
  be determined by
• R
• Where
• ? ( )
• L
• A

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Ex. Resistance Resistivity

• What would happen to the resistance in a wire if
  the length were increased?
• It would decrease.
• It would increase.
• It would remain the same.
• What would happen to the resistance in a wire if
  the cross-sectional area were increased?
• It would decrease.
• It would increase.
• It would remain the same.
• What would happen to the resistivity the length
  were increased?
• It would decrease.
• It would increase.
• It would remain the same.

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Low Resistance vs. High Resistance

• To Summarize
• wires make good conductors.
• While wires make poor conductors.

Low Resistance
High Resistance
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Resistance vs. Length and Resistance vs.
X-Sectional Area

• What is the relationship between

Resistance and Length? Resistance and X-Sectional Area?
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Resistivity vs. Temperature
Note The Resistivity is at ,
therefore, the resistance is also .
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How fast do the electrons travel?

• A simple observation would tell an observer that
  the flow of electricity appears to be
  instantaneous when flipping on a light switch.
• Does that mean the electrons travel at the speed
  of light?

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Drift Velocity

• When an electric field is applied to a conductor,
  it will set the electrons in motion in an overall
  direction the applied field.
• While the electric field travels at nearly
  the of , the overall speed of the
  electron from one end of the conductor to the
  other is quite slow and random in direction due
  to .

e
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Determining the drift velocity in a wire.

• The total charge in a section of wire can be
  determined as follows
• Where
• n
• A
• L
• e

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Determining the drift velocity in a wire.

• Since all the electrons move along the conductor
  at the same average drift speed, the total amount
  of charge that moves through a cross section of
  wire is
• Where the time it takes for the total charge to
  move through any cross section can be found by
• Where vd .

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Determining the drift velocity in a wire.

• Substituting (1) into (2) for q, and (3) into (2)
  for q, and then solving for vd gives us
• The number of charge carriers per unit volume (n)
  can be found as follows
• Where NA
• M
• ?

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Example Drift Velocity

• What is the drift velocity in the copper wires
  leading to a kitchen appliance that operates at 1
  Ampere?
• Note wire in your kitchen has to be capable of
  carrying 20 amps of current, therefore, it is
  specified to be 12 gauge.
• The cross-sectional area of 12 gauge wiring is
  3.31 x 10-6 m2
• Assume that 1 electron is donated by each atom.
• The density is 8.96 x 103 kg/m3.
• The atomic mass is 63.546 g/mole.

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Finding the Drift Velocity in a Copper Wire

• First determine the number of charges per unit of
  volume (n)
• Now determine the drift velocity (vd)
• Thats only m/hr!

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Power

• Power Rate at which work is done where
• P 1 / 1
• P (1 )(1 ) 1

Since V and I P P

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Example (Power)
What is the power rating of a lightbulb in
circuit where the current is 0.50 A and the
voltage is 120V?
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Power vs. Current and Power vs. Voltage (Ohmic
Materials)

• What is the relationship between
• power and current? Power and voltage?

P
P
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Energy

• Since power is the rate at which work is done the
  amount of energy required to complete a task is
  as follows
• Total Energy x
• W

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Example (Energy)
How much energy is consumed by a lightbulb
operating in circuit where the current is 0.50 A
and the voltage is 120V for 1 hour?
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Key Ideas

• A circuit is a closed path where current can
  flow.
• Current is the flow of charge.
• Resistance is the hindrance to the flow of
  charge.
• Ohms Law voltage to current ratio (V/I)
  Resistance.
• Resistivity is an intrinsic property of a
  material that is proportional the the resistance.
  
• An increase in length of a conductor will
  increase resistance.
• An increase in cross-sectional area of a
  conductor will decrease resistance.
• Power equals the rate at work is done and is
  represented electrically by P IV.