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 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 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? 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: Therefore, 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.