Ch 18: Electric currents

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Ch 18 Electric currents

• Charges in motion

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How is this different from static?

• Recall that a buildup of charges on an object is
  called Static electricity. This buildup will
  continue until an opportunity for discharge
  arrives. THEN we SEE the discharge as a spark
  (light lightning)
• In 1752 Benjamin Franklins famous kite
  experiment showed that lightning is an electric
  discharge- a giant spark.

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Steady now

• The transition from static electricity to flow of
  electric charge was sparked by the invention of
  the electric battery by Alessandro Volta
  (1745-1827) in 1800.
• The steady electric current flowing
  from this source transformed
  our civilization.

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Electric Battery

• The discovery of the battery came about as
  a result of an argument between Luigi Galvani
  and Volta. In the 1780s Galvani connected 2
  different metals to a frogs leg muscle and a
  static electricity machine.
• Volta proved that the electricity was not due to
  the animal cells, but rather due to two different
  metals using the frogs leg as an electrolyte.
  The source of the electricity was in the
  different metals.

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Alessandro Voltas Pile (Battery)

• Volta found certain combinations of metals
  produced greater effects than others. He listed
  an electrochemical series and found carbon
  could be used in place of one metal.
• He put a piece of cloth soaked in a salt solution
  between 2 metals and piled a battery of such
  couplings on top of each other. This pile or
  battery produced much more potential difference.

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Volta leads the way

• Scientists eventually realized the battery
  produces electricity by transforming chemical
  energy into electrical energy.
• Simplest batteries contain 2 plates (different
  metals) called electrodes, immersed in a solution
  called the electrolyte. This is called an
  electric cell.
• Several cells connected together is called a
  battery.

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How does the battery cell work?

• The electrodes dissolve in the acidic
  electrolyte. Zn leaves behind 2 electrons and
  enters the solution as positive. The zinc
  electrode then acquires a negative charge.
• As the solution becomes more positive, it pulls
  electrons off the carbon electrode, making it
  acquire a positive charge.
• Opposite charges develop a potential difference
  between the terminals and this is maintained
  until a conductor is connected between them.
  (See pg 529)

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How long will charge flow?

• After some time, one of the electrodes is used up
  and the cell becomes dead.
• The voltage between the battery terminals depends
  on what materials are used and their ability to
  be dissolved or give up electrons.
• Connecting batteries so the positive terminal of
  one touches the negative terminal of the other is
  in series and their voltages add up.

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Electric Current

• An electric circuit is a continuous conducting
  path between the terminals of a battery.
• A battery symbol is represented by
• Longer line positive terminal, shorter
  negative terminal.
• A flow of charge through the battery and wires of
  a complete path is called electric current.

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Charge it up

• Electric Current in a wire is the net amount of
  charge that passes through a wire per unit of
  time at any point.
• Average current, I is defined as
  where Q is the charge passing through the
  conductor in any time interval t.
• Electric current is measured in coulombs/second
  or amperes (abbrev amps or A).

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Conservation of Charge

• Charge doesnt disappear when it flows through a
  circuit.
• For any single circuit, the current at any
  instant is the same at one point as it is at any
  other point. This is the Conservation of
  Electric charge.
• Current is the flow of charge through a circuit.

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Example 18-1

• A steady current of 2.5A flows in a wire for 4.0
  min. (a) How much charge passed through any
  point in the circuit? (b) How many electrons
  would this be?

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18-1 Solution

• (a) Since the current was 2.5A or 2.5 C/s, then
  in 4.0 mins (240 seconds) the total charge that
  flowed was
• ?Q (2.5 C/s) (240s) 600 C
• (b) The charge on one electron is 1.60x10-19 C so
  600 C would consist of

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See Conceptual Ex 18-2

• Whats wrong with each scheme in trying to light
  a light bulb with a flashlight battery and a
  single wire? You try it
• How many ways can this be done? Choose a partner
  and figure it out.

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Conduction, duction whats your function?

• Conductors contain many free electrons.
• When a potential difference (voltage) is
  established across a circuit (complete closed
  conducting path), it is electrons that actually
  flow in the wire.
• Conventions of electric current many years ago
  decided conventional current is the direction
  positive charge will move. (From to -) but is
  equal to the negative charge flowing from to .

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Ohms Law Resistance and Resistors

• Georg Simon Ohm (1787-1854) was the first to
  establish experimentally that current, I, is
  directly proportional to the potential
  difference, V, applied to the ends of a wire.
• One source of potential difference is a battery.

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Current flowin

• Compare current in a wire to the flow of water in
  a river or pipe. In order to get current to
  flow a difference in potential between the ends
  must exist. (ie tip the pipe, gravity pulls
  water downhill.)
• How much current flows in a wire depends on the
  voltage, but also on the resistance. More
  resistance, like junk in a river, means less
  current.

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Ohms Law
Ohms Law establishes a relationship between
current, voltage, and resistance in a circuit.
Current, I, is equal to Voltage / Resistance.
Resistance is measured in ohms. Current is
measured in amps. Potential difference is
measured in volts.
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Example 18-3 Bulb Resistance

• A small flashlight bulb draws 300mA from its 1.5
  V battery. (a) What is the resistance of the
  bulb? (b) If the voltage dropped to 1.2 V, how
  would the current change?

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18-3 Solution

• (a) We use Ohms law and find RV / I
• R 1.5 V / 0.30 A 5.0 O
• (b) If the resistance stayed constant, the
  current would be approximately I V / R
• I 1.2 V / 5.0 O 0.24 A

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More on Resistance

• All electronic devices from wires to heaters to
  stereo amplifiers to lights offer resistance to
  the flow of current.
• In many circuits, resistors are used to control
  the amount of current.
• Two main types of resistors are wire wound
  resistors and composition resistors (which have
  color codes marking levels of resistance.)

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Your turn to Practice

• Please do ch. 18 Review pg 551 s 1-10

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Resistivity

• Resistance of a wire is directly proportional to
  its length, L and inversely proportional to its
  cross-sectional area, A. (A thicker wire has
  less resistance because there is more room for
  electrons to pass and a longer wire has greater
  resistance because there are more obstacles to
  electron flow.
• The third factor is a proportionality constant,
  ?, called resistivity, and depends on material
  type.
• Low R good conductor.

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Ex 18-4 Speaker Wires

• Suppose you want to connect your stereo to remote
  speakers. (a) If each wire must be 20m long,
  what diameter of copper wire should you use to
  keep the resistance less than 0.10O per wire?
  (b) If the current to each speaker is 4.0A, what
  is the voltage drop across each wire?

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18-4 Solution

• (a) We solve for the area A and use table 18-1
• The cross-sectional area of a wire is related to
  its diameter by Apd2/4. The diameter must then
  be at least
• (b) From Ohms Law, VIR (4.0A)(0.10O) 0.40 V

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Resistivity

• The resistivity of a material depends on
  temperature in that resistance of metals
  increases with temperature. At higher speeds,
  atoms are moving faster and interfere with each
  other more with the flow of electrons.
• There is a temperature coefficient of
  resistivity, a, that is given in Table 18-1 for
  various materials.

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Electric Power

• Electric energy can be transformed into other
  forms of energy such as thermal energy or light
  because the current is large and many collisions
  occur in tiny wire filaments or heating elements.
  (Low resistances of up to a few hundred ohms)
• During collisions KE of atoms increases and thus
  temperature increases.

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Electric Power

• Power is the rate at which energy is transformed.
  P (QV)/t.
• Recall charge flowing per second is current IQ/t
  so it follows that Power I V
• SI unit of Power is the same for any kind, watt.
  (1W1J/s)
• PIV I(IR) I2R (V/R)V V2/R
• Remember PIVVIR PIV, VIR

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Ex 18-7 Headlights

• Calculate the resistance of a 40 W automobile
  headlight designed for 12 V.
• SOLN R V2/P
• R (12V)2 / (40W) 3.6O
• This is the resistance when the bulb is burning
  brightly at 40 W. When the bulb is cold, the
  resistance is lower and since the current is
  high, most bulbs burn out when first turned on.

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Electric Energy

• Our electric bill costs us money based on the
  electric energy we use, not just power.
• Since Power is the rate energy is transformed,
  electric energy is just Power time the power is
  used.
• EPt (kilowatthours) 1kWh1000W3600s 3.6x106
  J.

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Ex 18-8 Electric Heater

• An electric heater draws 15.0A on a 120 V line.
  How much power does it use and how much does it
  cost per month (30days) if it operates 3.0 h per
  day and the electric company charges 10.5 cents
  per kWh?
• Solution PIV (15.0A)(120V) 1800 W
• To operate per month (3h/d)(30d)90hrs so it
  would cost (1.80kWh)(90h)(0.105)17.

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Ex 18-9 Lightning Bolt

• A typical lightning bolt can transfer 109 J of
  energy across a potential difference of perhaps 5
  x 107 V during a time interval of 0.2s. Use this
  information to estimate the total amount of
  charge transferred, the current, and the average
  power over the 0.2s.

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18-9 Soln

• Energy QV so
• The current over the 0.2s is about
• The average power delivered is Pavg energy/time
• Which can also be found by PIV100A(5x107 V)5GW

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Power in Household Circuits

• If current in wires gets too large, the wires get
  hot (produce thermal energy at a rate of I2 R).
  Wires in walls of a building can get so hot
  start a fire.
• Buildings should be designed to handle any
  expected load prevent overloading. (Carrying
  more current than is safe)
• Fuses and circuit breakers are devices used to
  help prevent overloading. This occurs when too
  many devices draw current in that area OR when
  wires are faulty.

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Household Power

• Household circuits are designed so every device
  connected receives the standard voltage (120V in
  the US).
• These circuits are typically arranged parallel
  (more later).
• Total current in a circuit that blows should
  be checked!
• Never replace a properly rated fuse with a higher
  one!

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Open circuits

• A blown fuse or breaker will open a circuit so
  there is no longer a complete conducting path and
  current will not flow.

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Alternating Current

• When a battery is connected to a circuit, current
  flows steadily in one direction. This is called
  direct current, DC.
• Electric generators (power plants) produce
  alternating current, AC.
• AC reverses directions many times each second and
  is sinusoidal (creates sine wave) Current
  supplied to homes and businesses around the world
  is ac.

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AC

• AC voltage oscillates between V0 and V0 where
  V0 is referred to as peak voltage.
• As a function of time, the voltage can be found
  by VV0 sin2pft.
• The frequency, f, is the number of complete
  cycles per second and in the US and Canada is 60
  Hz. Some countries use 50Hz.

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Your turn to Practice

• Complete the wksh for series circuits given in
  class.
• Please do Ch 18 Review pg 551 s 11, 12, 13
• Please do Ch 18 Review pg 552 s 23, 24, 27