Electrical Power

1
Electrical Power

• From Power Plant to Toaster

2
Electrical Power

• Electrical power is transferred by electrons
  through a circuit
• The total power consumed by an appliance depends
  on how much voltage and current it uses
• In equation form
• P I x V
• P is power in watts
• I is current in amps
• V is voltage in volts

3
Power Loss in a Resistor

• When electric current passes through a resistor,
  it converts power to heat
• Using Ohms law, the power loss in a resistor is
• P I2 x R
• where
• P is power in Watts
• I is current in Amps
• R is resistance in ohms

4
Appliance Ratings

• Most appliances are labeled so that one can
  calculate their power consumption
• Two types of labeling
• Power and voltage
• Voltage and current
• Power, voltage, current and resistance can all be
  calculated from the appliance label!

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Example 1

• Here, voltage (120 V) and power (18 W) are
  labeled
• What current does this VCR use and what is its
  resistance?
• Current from P IV we know I P/V so
• I (120 V)/(18 W) 6.7 A
• Resistance from V IR we know R V/I so
• R (120 V)/(6.7 A) 18 ?

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Example 2

• Here, voltage (120 V) and current (300 mA) are
  labeled
• How much power does this VCR use and what is its
  resistance?
• Power from P IV
• P (120 V)/(0.3 A) 36 W
• Resistance from V IR we know R V/I so
• R (120 V)/(0.3 A) 400 ?

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Basic Laws of Electricity
Ohms Law V IR
Electric Power P VI
Power Loss P I2 R

• In many appliances, lost power is actually
  converted into useful energy
• Example A stereo converts most of the power
  loss to sound

8
AC and DC

• In a dc (Direct Current) electrical system, the
  voltage remains constant
• In an ac (Alternating Current) electrical system,
  the voltage fluctuates rapidly from positive to
  negative values
• In a household electrical outlet (which is AC),
  the voltage fluctuates from -120 V to 120 V
  sixty times every second

9
Why Two Types of Current?

• dc is better when
• an appliance needs to run on batteries because
  batteries produce dc currents
• an appliance uses integrated circuits (e.g.
  computer chips) because most chips are designed
  to run with 5 V or 12 V dc
• ac is better when
• high voltages are required because the voltage
  can be changed using a simple device called a
  transformer
• the appliance needs to run a motor because ac
  motors are easier to build

10
A Brief History of Electricity

• Electricity was first studied in detail in the
  18th century
• Many practical uses for electricity (e.g. the
  light bulb) were invented by Thomas Edison in the
  late 19th century
• Edison (an inventor) co-founded Edison Electric
  (now General Electric), which used dc

• Nikola Tesla (a physicist) helped to found
  Westinghouse, which used ac
• To prove that ac is dangerous, Edison built an
  electric chair (which was used)
• Eventually, ac became the industry standard
  because ac can be efficiently transferred over
  large distances

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How to Transfer Electrical Power

• Wires used to transfer electrical power have a
  small resistance R
• Power loss (P I2R) is greater when the current
  I is large
• High voltage is better because more power can be
  transferred with less current

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Example 1

• A power plant want to transfer 1 MW through a
  line with a resistance of 1 ?
• Case 1 The voltage is 1200 V, what is the power
  loss?
• Answer First find the current using P IV
• which is the same as I P/V
• so I (1,000,000 W)/(1200 V) 833 A
• the power loss is P I2R
• so P (833 A)2(1 ?) 693,000 W !!!!

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Example 2

• A power plant want to transfer 1 MW through a
  line with a resistance of 1 ?
• Case 2 The voltage is 120,000 V, what is the
  power loss?
• Answer First find the current using P IV
• which is the same as I P/V
• so I (1,000,000 W)/(120,000 V) 8.33 A
• the power loss is P I2R
• so P (833 A)2(0.1 ?) 69.4 W !!!!

14
Transformers

• Transformers are simple, reliable devices that
  change the voltage
• When voltage goes up, current goes down and visa
  versa--power remains the same
• Transformers only work for ac circuits
• Transformers are constructed by simply winding
  wire around two ends of a rectangular piece of
  metal

Voltage In
Voltage Out
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Types of Transformers

• Step-up transformers convert low voltages to high
  voltages used between power plant and power
  lines
• Step-down transformers convert high voltages to
  low voltages used just outside your home and in
  small appliances

Step-up
Step-down
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How Electricity Gets to Your House

• A power plant generates 24,000 V
• A power station steps up the voltage to 230,000 V
  (so it can be transferred through power lines)
• A substation steps the voltage down to 100,000 V
• A distributing substation steps the voltage down
  to 20,000 V
• A step down transformer outside your house steps
  the voltage down to 120 V and 240 V (240 V is for
  large appliances like your washer and dryer)

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Why not Transfer Electricity at a Billion Volts?

• For one thing, air is not a perfect insulator
• At very high voltages, arcs of lightning would
  shoot between power lines and the ground
• Safety is also an issue
• (Note birds can land on a bare wire because they
  do not create a closed circuit, i.e. a path to
  the ground)

18
Do Electromagnetic Waves from Power Lines Cause
Cancer?

• No because
• low frequency electromagnetic waves (i.e. 60 Hz)
  cannot, even in theory, interfere with chemical
  reactions
• the intensity of the radiation is much less than
  the intensity of radiation already present in the
  body
• Note cell phones (which operate at millions of
  Hertz) cant cause cancer either