Ohms Law, Power, and Energy

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Chapter 4

• Ohms Law, Power, and Energy

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Ohms Law

• The current in a resistive circuit is directly
  proportional to its applied voltage and inversely
  proportional to its resistance.
• I E/R
• For a fixed resistance, doubling the voltage
  doubles the current.
• For a fixed voltage, doubling the resistance
  halves the current.

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Ohms Law

• Ohms Law may also be expressed as
  E IR and R E/I
• Express all quantities in base units of volts,
  ohms, and amps or utilize the relationship
  between prefixes.

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R 12 x 101 120? I V/R 12V/120? 0.1A
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Ohms Law in Graphical Form

• The relationship between current and voltage is
  linear.

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Open Circuits

• Current can only exist where there is a
  conductive path.
• When there is no conductive path we refer to this
  as an open circuit.
• If I 0, then Ohms Law gives R E/I E/0 ?
  infinity
• An open circuit has infinite resistance.

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Voltage Symbols

• For voltage sources, use uppercase E.
• For load voltages, use uppercase V.
• For AC voltages use lowercase e.g. v
• Since V IR, these voltages are sometimes
  referred to as IR drops.

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Voltage Polarities

• The polarity of voltages across resistors is of
  extreme importance in circuit analysis.
• Place the plus sign at the tail of the current
  arrow.

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Current Direction

• We normally show current out of the plus terminal
  of a source.
• If the actual current is in the direction of its
  reference arrow, it will have a positive value.
• If the actual current is opposite to its
  reference arrow, it will have a negative value.

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Current Direction

• The figures at right are two representations of
  the same current
• Conventional current is employed (opposite
  direction to electron flow.

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• R 6V/25mA
• 240?

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Power

• The greater the power rating of a light, the more
  light energy it can produce each second.
• The greater the power rating of a heater, the
  more heat energy it can produce.
• The greater the power rating of a motor, the more
  mechanical work it can do per second.
• Power is related to energy, which is the capacity
  to do work.

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Power

• Power is the rate of doing work.
• Power Work/time
• Power is measured in watts.
• One watt one joule per second

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Power in Electrical Systems

• From V W/Q and I Q/t, we get
• P VI
• From Ohms Law, we can also find that
• P I2R and P V2/R
• Power is always in watts, no matter which
  equation is used.

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Power in Electrical Systems

• We should be able to use any of the power
  equations to solve for V, I, or R if P is given.
• For example

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FIG. 4.13 Example 4.6.
Pin IV (120V)(5A) 600W
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Power Rating of Resistors

• Resistors must be able to safely dissipate their
  heat without damage.
• Common power ratings of resistors are 1/8, 1/4,
  1/2, 1, or 2 watts.
• A safety margin of two times the expected power
  is customary.
• An overheated resistor is often the symptom of a
  problem rather than its cause.

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Energy

• Energy Power time
• Units are watt-seconds, watt-hours, or more
  commonly, kilowatt-hours.
• Energy use is measured in kilowatt-hours by the
  power company.
• For multiple loads, the total energy is the sum
  of the energy of the individual loads.

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Energy

• Cost Energy cost per unit or
• Cost Power time cost per unit
• To find the cost of running a 2000-watt heater
  for 12 hours if electric energy costs 0.08 per
  kilowatt-hour Cost 2kW 12 hr 0.08
  Cost 1.92

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Law of Conservation of Energy

• Energy can neither be created nor destroyed, but
  can be converted from one form to another.
• Examples Electric energy into heat Mechanical
  energy into electric energy
• In energy conversions, some energy may be
  dissipated as heat, giving lower efficiency.

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Efficiency

• Poor efficiency in energy transfers results in
  wasted energy.
• An inefficient piece of equipment generates more
  heat this heat must be removed.
• Heat removal requires the use of fans and heat
  sinks.

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Efficiency

• Efficiency will always be less than 100.
• Efficiencies vary greatly power transformers may
  have efficiencies of 98, while amplifiers have
  efficiencies below 50.
• To find the total efficiency of a system
• ?Total ?1 ?2 ?3

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• ?1 x ?2
• 0.9 x 0.7
• 0.63
• 63

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FIG. 4.16 Kilowatthour meters (a) analog
(b) digital.
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FIG. 4.19 Basic components of a generating
system.
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Fuses (a) CC-TRON (0-10 A) (b) Semitron
(0-600 A) (c) subminiature surface-mount chip
fuses.
Fuses
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Circuit breakers.
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FIG. 4.23 Ground fault circuit interrupter
(GFCI) 125 V ac, 60 Hz, 15 A outlet.