Current Electricity

1
Current Electricity
2
Define an electric current and the ampere

• A flow of charged particles is called an electric
  current.
• Your textbook defines the direction of current
  flow in a circuit to be from the positive
  terminal of the battery to the negative terminal.
  
• You can consider the positive terminal to have a
  build up of potential energy and the negative
  terminal to be have a deficit of potential energy.

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Contd

• Electric current is measured in Amperes (A).
• An ampere is a flow of one Coulomb per second.

4
Contd

• Charges move as a result of a potential
  difference.
• In order to have a current, a difference of
  potential must be maintained.
• Something that provides a potential difference is
  known as a voltage source.
• A battery is an example of a voltage source.

5
Contd

• The voltage of the battery is the amount of work
  done per Coulomb of charge.
• Voltage sources only maintain the difference in
  potential in the circuit.
• They do not provide the charges that move in
  response to this difference in potential.

6
Contd

• The charges that move are those already found in
  the conductors of the circuit.
• The charges themselves move at a drift velocity
  of 1 mm/s however the potential difference that
  causes them to start moving travels at the speed
  of light, 3 108 m/s.

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Define capacitance

• Capacitance is the ratio of the charge on a body
  to its potential.
• Capacitance in measured in units of Farads.

8
Contd

• Farad is a very large amount of capacitance so
  you are typically dealing with capacitances in
  the micro and pico Farad range.
• Micro is 10-6
• Pico is 10-12

9
Contd

• A device that is designed to have a specific
  capacitance is called a capacitor.
• All capacitors are made of two conducting plates
  separated by an insulator called a dielectric.
• The two conductors have equal and opposite
  charges.

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Contd

• C capacitance (F)
• q charge (C)
• V voltage (V)

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Sample Problem

• A 3?F capacitor is connected to a 12-V battery.
  How much charge is put on each plate by the
  battery?
• 3.6 10-5 C
• What is the charge on a 12 ?F capacitor if it is
  connected to an 18-V battery?
• 2.16 10-4 C

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Capacitors for energy storage

• Electrical energy can be stored in capacitors.

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Contd

• W Work or Energy (J)
• C capacitance (F)
• V voltage (V)

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Sample Problem

• Find the amount of energy stored in a 5 ?F
  capacitor when it is connected across a 120-V
  line.
• 0.036 J

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simple electric circuits

• An electric circuit is a continuous path through
  which electric charges can flow.
• An electric circuit consists of a source of
  potential difference (battery), a load or device
  that uses the energy (light, stereo, etc), and
  conductors creating a continuous path (wires).

16
Contd

• A schematic diagram uses symbols rather than
  pictures to represent the components of an
  electric circuit.
• You will have a closed notes quiz over the
  schematic symbols.

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Resistor
Battery
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Voltmeter
19
Contd

• As a charge moves through resistors in a circuit,
  its potential energy is reduced.
• The energy used as the charge moves around the
  remainder of the circuit is equal to the amount
  of work done to give the charge its initial
  energy.
• Therefore, the total voltage drop going around
  the circuit is equal to the amount of potential
  difference across the battery.

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understanding of the instrumentation to measure V
and I

• A voltmeter is a device that measures the
  difference in potential across two points in an
  electric circuit, typically across a resistor.
  Voltmeters are connected in parallel.

21
Contd

• An ammeter is a device that measures the current
  flowing through a point in the circuit. Ammeters
  are connected in series.

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Define resistance

• Resistance is the opposition to the electric
  current flow.
• The unit of resistance is the Ohm (?).
• Various factors affect the resistance of a
  conductor temperature, length, cross-sectional
  area, and nature of the material.
• Resistance is lower at colder temperatures.

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Contd

• On the resistor itself is a series of colored
  bands. These colored bands represent the value
  of the resistance.
• Bad Boys Race Our Young Girls But Violet
  Generally Wins
• Black Brown Red Orange Yellow
• 0 1 2 3
  4
• Green Blue Violet Grey White
• 5 6 7 8 9

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Contd

• 10 for example a resistor with the
  colored bands of blue brown red would have a
  value of 61 102 or 6100 Ohms.

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Contd

• For a conductor resistance can be calculated.
• R resistance (?)
• ? resistivity (?mm)
• l length (mm)
• A cross sectional area (mm2)

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Sample Problem

• Calculate the resistance of a piece of aluminum
  whose resistivity is 2.824 10-6 ??cm that is 10
  cm long and has a cross-sectional area of 100
  mm2.
• 2.824 10-5 ?
• The resisitivity of nickel silver is 49 10-6
  ??cm. Calculate the resistance per unit length
  of a 22-gauge nickel-silver wire of radius 0.321
  mm.
• 0.00151 ?/m

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Describe Ohms law

• Ohms law can also be used to calculate
  resistance.
• A conductor which follows Ohms law is said to be
  an Ohmic conductor.

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Contd

• Most metallic conductors follow Ohms law over a
  limited range of voltages when held at a constant
  temperature.
• Resistance is the ratio of potential difference
  across the conductor to the current flow through
  it.

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Contd

• I current (A)
• V Voltage (V)
• R resistance (?)

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Sample Problem

• All electric devices are required to have an
  identifying plate that specifies their electrical
  characteristics. For example, the plate on a
  certain steam iron states that the iron carries a
  current of 6 A when connected to a 120-V source.
  What is the resistance of the steam iron?
• 20 ?
• The resistance of a hot plate is equal to 40 ?.
  How much current does the plate carry when
  connected to a 120-V source?
• 3 Amps

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definition of power

• Power is the rate at which energy is transmitted.
  
• Power is measured in Watts (W).

34
Contd

• P Power (Watts)
• V Voltage (V)
• I Current (A)
• R Resistance (Ohms)

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Sample Problems

• An electric heater is constructed by applying a
  potential difference of 50 V to a nickel-silver
  wire of total resistance 8 ?.
• (a) Find the current carried by the wire
• 6.25 Amps
• and the power rating of the heater.
• 312.5 Watts
• (b) If we were to double the applied voltage to
  the heater, what would happen to the current
• double
• and the power?
• quadruple

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Sample Problems

• What power is supplied to a lamp that is operated
  by a battery having a 12-V difference of
  potential across its terminals when the current
  through the lamp is 2.0 A?
• 24 Watts
• How much electrical energy has been supplied to
  the lamp after it has been operating for 4.0 s?
  Hint Think about formulas from last semester.
• 96 Joules

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Contd

• E Energy (J)
• W Work (J)
• V Voltage (V)
• q Charge (C)

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Energy Conversions

• A motor converts electrical energy into
  mechanical energy.
• An electric lamp changes electrical energy into
  light.
• Any time an energy conversion occurs some of the
  energy is converted into excess thermal (heat)
  energy.

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Contd

• Some devices are designed to convert electrical
  energy into thermal energy such as a heater or
  toaster.
• A heater needs to have high resistance wires that
  also have a high melting point.

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high-voltage lines

• Electrical energy must often be transmitted over
  long distances to reach homes and industries.
• In order to reduce thermal energy losses in
  supply lines either the current or the resistance
  must be reduced.
• To reduce resistance, large diameter cables of
  high conductivity are used.
• Increasing the voltage can reduce the current.

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• Thermal energy losses can be calculated using the
  formulas

E Work or Energy (Joules) P Power (Watts) V
Voltage or Potential Difference (Volts) I
Current (Amperes) R Resistance (Ohms) t time
(seconds
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Sample Problems

• A calculator draws 3.0 x 10-5 A of current when
  connected to a 9.0 V battery. How much energy
  does the calculator use if it is left on for 20.0
  minutes?
• 0.324 J

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Define the kilowatt-hour

• A kilowatthour is equal to 1000 Watts delivered
  continuously for 3600 seconds.
• It is a unit of work.

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Contd

• To calculate the cost of electrical energy, the
  energy must first be calculated (EPt) then
  converted to units of kilowatthours, then
  multiplied by the price per kilowatthour.

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• Bill total amount that needs to be paid ()
• price price (/kWh or per kiloWatt hour)
• P power (kW)
• T time (hours)

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Sample Problems

• The heating element in an electric toaster
  dissipates 1.37 kW of power as heat when
  connected across a 120-V line. What current is
  in the heating element?
• 11.42 Amps
• What is the resistance of the heating element?
• 10.51 Ohms
• What is the cost for 1.25 hours of operation at
  8.75 cents per kWh?
• 15 cents

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Sample Problems

• An electric heater has an element resistance of
  7.8 ? and when connected across a source of
  voltage draws a current of 15.0 A. What is the
  potential difference across the heater element?
• 117 Volts
• What is the cost for 8.0 hours of operation at
  9.25 cents per kWh?
• 130 cents 1.30