Vern J. Ostdiek
Donald J. Bord
Chapter 7
Electricity
(Section 5)
7.5 Power and Energy in Electric Currents
• Because a battery or other electrical supply must
continually put out energy to cause a current to
flow, it is important to consider the power
output—
•
the rate at which energy is delivered to the circuit.
• The power is determined by the voltage of the
power supply and the current that is flowing.
• Think of it this way:
•
•
the power output is the amount of energy expended
per unit amount of time.
The power supply gives a certain amount of energy
to each coulomb of charge that flows through the
circuit.
7.5 Power and Energy in Electric Currents
• Consequently, the energy output per unit time
equals the energy given to each coulomb of
charge multiplied by the number of coulombs that
flow through the circuit per unit time:
energy per unit time energy per coulomb
= number of coulombs per unit time
7.5 Power and Energy in Electric Currents
• These three quantities are just the power, voltage,
and current, respectively.
•
Consequently, the power output of an electrical
power supply is
power = voltage ´ current
P =VI
•
The units work out correctly in this equation also:
joules per coulomb (volts) multiplied by coulombs
per second (amperes) equals joules per second
(watts).
• The power output of a battery is proportional to the
current that it is supplying:
•
the larger the current, the higher the power output.
7.5 Power and Energy in Electric Currents
Example 7.4
• In Example 7.1, we computed the current that
flows in a flashlight bulb.
•
What is the power output of the batteries?
• Recall that the batteries produce 3 volts and that
the current in the lightbulb is 0.5 amperes.
•
The power output is
P =VI = 3 V ´ 0.5 A
= 1.5 W
•
The batteries supply 1.5 joules of energy each
second.
7.5 Power and Energy in Electric Currents
• What happens to the energy delivered by an
electrical power supply?
• In a lightbulb, less than 5 percent is converted into
visible light, and the rest becomes internal energy.
•
Even the visible light emitted by a lightbulb is
absorbed eventually by the surrounding matter and
transformed into internal energy. (Interior lighting is
actually used to heat some buildings.)
7.5 Power and Energy in Electric Currents
• Electric motors in hair dryers, vacuum cleaners,
and the like convert about 60 percent of their
energy input into mechanical work or energy while
the remainder goes to internal energy.
•
The mechanical energy is generally dissipated as
internal energy through friction.
• In a similar way, we can trace the energy
conversions in other electrical devices and the
outcome is the same: most electrical energy
eventually becomes internal energy.
7.5 Power and Energy in Electric Currents
• Ordinary metal wire converts electrical energy into
internal energy whenever there is a current
flowing.
•
You may have noticed when using a hair dryer that
its cord becomes warm.
• This heating, called ohmic heating, occurs in any
conductor that has resistance, even when the
resistance is quite small.
•
•
The huge cables used to conduct electricity from
power plants to cities are heated by this effect.
This heating represents a loss of usable energy.
7.5 Power and Energy in Electric Currents
• The temperature that a current-carrying wire
reaches from ohmic heating depends on the size
of the current and on the wire’s resistance.
Increasing the current in a given wire will raise its
temperature.
• Many devices utilize this effect.
•
The resistances of heating elements in toasters and
electric heaters are chosen so that the normal
operating current is large enough to heat them until
they glow red hot and can toast bread or heat a
room.
7.5 Power and Energy in Electric Currents
• The filament in an incandescent lightbulb is made
so thin that ohmic heating causes it to glow white
hot and emit enough light to illuminate a room.
7.5 Power and Energy in Electric Currents
• Ohmic heating is a major consideration in the
design of sophisticated integrated circuit chips.
•
Even though the currents flowing through the tiny
transistors are extremely small, there are so many
circuits in such a small space that special steps
must be taken to make sure the heat produced is
conducted away.
7.5 Power and Energy in Electric Currents
• Because a superconductor has zero resistance,
there is no ohmic heating.
• The overall efficiencies of most electrical devices
could be improved if regular wires could be
replaced by superconductors.
•
•
Superconducting transmission lines would allow
electricity to be carried from a power plant to a city
with no loss of energy.
The limitations of currently known superconductors,
however, make such uses impracticable.
7.5 Power and Energy in Electric Currents
• A sufficiently large current in any wire can cause it
to become very hot—hot enough to melt any
insulation around it or to ignite combustible
materials nearby.
• Fuses and circuit breakers are put into electric
circuits as safety devices to prevent dangerous
overheating of wires.
•
If something goes wrong or if too many devices are
plugged into the circuit and the current exceeds the
recommended safe limit for the size of wire used,
the fuse or circuit breaker will automatically “break”
the circuit and the current will stop.
7.5 Power and Energy in Electric Currents
• A fuse is a fine wire or piece of metal inside a
glass or plastic case.
•
When the current exceeds the fuse’s design limit,
the metal melts away, and the circuit is broken.
7.5 Power and Energy in Electric Currents
• Designers of electric circuits in cars, houses, and
other buildings must choose wiring that is large
enough to carry the currents needed without
overheating.
•
They must also include fuses or circuit breakers
that will disconnect a circuit if it is overloaded.
• Most electrical devices are rated by the power that
they consume in watts.
•
The equation P = VI can be used to determine how
much current flows through the device when it is
operating.
7.5 Power and Energy in Electric Currents
Example 7.5
• An electric hair dryer is rated at 1,875 watts when
operating on 120 volts.
•
What is the current flowing through it?
P = VI
1,875 W = 120 V ´ I
1,875 W
=I
120 V
I = 15.6 A
•
The wires in the electric cord must be large enough
to allow 15.6 amperes to flow through them without
becoming dangerously hot.
7.5 Power and Energy in Electric Currents
• The highest current that can flow in a particular
wire without causing excessive heating depends
on the size of the wire.
•
This is one reason why electric utilities use high
voltages in their electrical power supply systems.
The electricity delivered to a city, subdivision, or
individual house must be transmitted with wires.
• Because P = VI, using a large voltage makes it
possible to transmit the same power with a smaller
current.
•
If low voltages were used, say, 100 volts instead of
the more typical 345,000 volts, much larger cables
would have to be used to handle the larger
currents.
7.5 Power and Energy in Electric Currents
• Customers pay for the electricity supplied to them
by electric companies based on the amount of
energy they use.
•
An electric meter keeps track of the total energy
used by monitoring the power (rate of energy use)
and the amount of time each power
level is maintained.
7.5 Power and Energy in Electric Currents
• Recall the equation used to define power:
P=E t
• Therefore,
E = Pt
•
•
The amount of energy used is equal to the power
times the time elapsed.
If P is in watts and t is in seconds, then E will be in
joules.