chapter 4 ohm’s law, power, and energy. 2 ohm’s law current in a resistive circuit –directly...
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Chapter 4
Ohm’s Law, Power,
and Energy
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Ohm’s Law• Current in a resistive circuit
– Directly proportional to its applied voltage – Inversely proportional to its resistance
R
EI
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Ohm’s Law
• For a fixed resistance– Doubling voltage doubles the current
• For a fixed voltage– Doubling resistance halves the current
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Ohm’s Law• Also 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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Ohm’s Law in Graphical Form• Linear relationship between current and
voltage• y = mx
– y is the current– x is the voltage– m is the slope
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Ohm’s Law in Graphical Form• Slope (m) determined by resistor
conductance
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Ohm’s Law in Graphical Form
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Open Circuits• Current can only exist where there is a
conductive path
• Open circuit– When there is no conductive path
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Open Circuits
• If I = 0– Ohm’s Law gives R = E/I = E/0 infinity
• An open circuit has infinite resistance
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Voltage Symbols• Voltage sources
– Uppercase E
• Voltage drops– Uppercase V
• V = IR– IR drops
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Voltage Polarities
• Polarity of voltage drops across resistors is important in circuit analysis
• Drop is + to – in the direction of conventional current
• To show this, place plus sign at the tail of current arrow
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Voltage Polarities
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Current Direction• Current usually proceeds out of the
positive terminal of a voltage source
• If the current is actually in this direction, it will be supplying power to the circuit
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Current Direction• If the current is in the opposite direction
(going into the positive terminal), it will be absorbing power (like a resistor)
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Current Direction• See two representations of the same current on
next slide• Notice that a negative current actually proceeds
in a direction opposite to the current arrow
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Current Direction
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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
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Power• The greater the power rating of a motor,
the more mechanical work it can do per second
• Power is related to energy– Capacity to do work
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Power• Power is the rate of doing work
– Power = Work/time
• Power is measured in watts (W)
• Work and energy measured in joules (J)
• 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 Ohm’s Law, we can also find that
P = I2R and P = V2/R
• Power is always in watts
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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:
PRV
R
PI
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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
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Power Rating of Resistors
• A safety margin of two times the expected power is customary
• An overheated resistor– Often the symptom of a problem rather than
its cause
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Energy
• Energy = – Power × time
• Units are joules
• Watt-seconds– Watt-hours or kilowatt-hours
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Energy
• Energy use is measured in kilowatt-hours by the power company
• For multiple loads– Total energy is sum of the energy of
individual loads
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Energy
• Cost = – Energy × cost per unit or
• Cost = – Power × time × cost per unit
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Energy
• 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– Converted from one form to another
• Examples: – Electric energy into heat– Mechanical energy into electric energy
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Law of Conservation of Energy• 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– Heat must be removed
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Efficiency• Efficiency (in %) is represented by η
(Greek letter eta)– Ratio of power out to power
• Heat removal requires fans and heat sinks
%100P
P
in
out
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Efficiency• Always less than or equal to 100%
• Efficiencies vary greatly:– Power transformers may have efficiencies of
up to 98%– Some amplifiers have efficiencies below 50%
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Efficiency• To find the total efficiency of a system
– Obtain product of individual efficiencies of all subsystems:
Total = 1 × 2 × 3 × ∙∙∙