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Giancoli 5th Ch 18 p. 538 MHR Ch 15 p.734 Electric Power Electrical energy is used extensively in our lives since it is plentiful, relatively inexpensive, and easily transformed into other forms. In our homes, appliances such as ranges, dryers, toasters, and heaters transform electrical energy into thermal via a “heating element” i.e. a resistor Electric Power Power is defined as energy transformed per unit time P = E/t In electrical devices, charge is moved in a circuit by a voltage so, P = qV/t but I = q/t so P = IV. From Ohm’s law, V=IR so P = I(IR) = I2R. Furthermore, I=V/R, so P = (V/R)V = V2/R P=IV applies to any device, but I2R & V2/R only apply to resistors Examples A tail-light in my car is rated at 10. W and operates off the 12V battery. What resistance is offered by the tail- light? P = V2/R, so R = V2/P 12V2/(10.W) Shiva works in an office which has an electric heater connected to a 120 V line. The heater draws 15 A of current. How much power does it use and how much does it cost to run the heater per month if it runs for 3.0 h a day and if NS Power charges 12 ¢ per kWh ( kilowatt-hour- a unit of energy) Examples P =IV = (15A)(120V) = 1800 W = 1.8 kW Cost = (1.8kW)(3.0 h/day)(30. day/month)($0.12/kWh) Cost = $ 19.44 Power in household circuits The copper wiring in your home does offer some resistance to the flow of charge , but it is quite small, and copper is a good conductor. Because the wire has some resistance, if the current is large enough, there is a substantial heating effect in the wire i.e. P = i2R. If the wire gets hot enough, an electrical fire could start. A thicker wire (gauge) has a greater cross sectional area and can carry more current without overheating. When a circuit carries more current than is safe, we say it is “overloaded.” Power in household circuits To prevent overloading and the likelihood of electrical fires, fuses and circuit breakers are installed in the circuits. These are wired in to your electrical panel or fuse box. Circuit breakers and fuses are really just switches designed to open the circuit when a certain amount of current in the circuit is exceeded. Fuses have a metal ribbon which melts and opens the circuit. Circuit breakers are spring loaded switches which “trip” when the current is exceeded. They must be reset after being tripped. Power in household circuits- example A 100 W lightbulb, an 1800 W electric heater, a 350 W stereo receiver and a 1200 W hair dryer are all connected in parallel to a 120 V line with a 20 A breaker. Will the breaker be tripped? Item I=P/V I (Amps) Lightbulb 100W/120 V 0.80 A Heater 1800 W/120 V 15.0 A Receiver 350 W/120 V 2.9 A Hair Dryer 1200 W/120 V 10.0 A The total amps in the circuits is 0.80 + 15.0 + 2.9 + 10.0 = 28.7 A So the breaker will be tripped.
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