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 conductor was connected to
both plates?
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Creating a Circuit
The electrons would flow from the negatively
charged plate to the positively charged plate
until the amount of charge was the same for both
plates and the wire.
How do we maintain the flow of charge?
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Creating a Circuit

• Circuit
• A closed loop in which electric current can
  flow.
• It generally includes a device such as a light
  bulb that reduces the electric potential energy.
• It also includes a device to increase potential
  energy (Charge Pump).

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What is Current?

• Current is the rate of flow of charge.
• I q/t 1 Coulomb/second 1 Ampere (A)
• Conventional Current flow of positive charge.
  (Note that positive charges do NOT flow in
  metallic conductors.)
• Electron flow is simply the
• flow of electrons.

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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.
• R V/I
• Where
• R Resistance in Ohms (?)
• V Electric Potential in Volts (V)
• I Current in Amperes (A)
• Resistance is the hindrance to the flow of
  charge.
• Most metallic conductors obey Ohms Law.

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Ohms Law

• The resistance (R) represents the slope (m) of a
  curve where V is plotted against I.
• What is R?
• For Ohmic materials, the curve is a straight line.

10?
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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 electric field, but scatter in
  a very short time from things that get in the way
• defects, lattice vibrations (phonons), etc
• The more collisions, the greater the resistance
  and the fewer the collisions, the less the
  resistance.
• 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 conductive
  ability of the material.
• Resistivity is an intrinsic (natural) property of
  a material.
• The higher the resistivity, the higher the
  resistance and vice versa.
• For a conductor of length L (m) and
  cross-sectional area A (m2), the resistance can
  be determined by
• R ?L/A
• Where
• ? resistivity (?m)
• L length of the conductor
• A Cross-Sectional Area

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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
• Short fat wires make good conductors.
• While long skinny wires make poor conductors.

Short Fat Low Resistance
Long Skinny 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 zero at 0 K, therefore,
the resistance is also zero.
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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 opposite the applied field.
• While the electric field travels at nearly the
  speed of light, the overall speed of the electron
  from one end of the conductor to the other is
  quite slow and random in direction due to
  collisions.

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 number of carriers per unit volume
• A cross-sectional area
• L length of the conductor
• e charge of an electron (the elementary charge)

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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
• Since v d/t, we can find the time it takes for
  the total charge to move through any cross
  section by
• Where vd drift velocity and L length of wire.

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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 Avogadro's Number
• M the atomic mass number
• ? density

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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 0.08 m/hr!

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Power

• Power Rate at which work is done where
• P VI
• P 1 Joule/second 1 Watt
• P VI (1 Volt)(1 Ampere) 1 Watt

Since V IR and I V/R P IRI I2R P VV/R
V2/R
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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? P VI P 120 V0.50 A P
60 VA 60 W
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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 I2R
P V2/R
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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 Power x time
• W Pt

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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? W VIt W
120 V0.50 A3600 s W 216,000 J W 216 kJ
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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.