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Average Power. Average Power. Instantaneous Power. FYI: Electrical power is measured in joules / second or watts , just as in mechanics. Topic 5.1 Extended B – Electric power.
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Average Power Average Power Instantaneous Power FYI: Electrical power is measured in joules/second or watts, just as in mechanics. Topic 5.1 ExtendedB – Electric power Back in the day when we talked about power we defined it more or less as the rate at which work is being done. Work time P = But in electricity we know that the work W in moving a charge q through a potential difference of V is given by Thus W = qV. qV t P = If the current I and the voltage V are constant, we can write the average power as the instantaneous power like this, P = IV P = I2R V2 R P = since I = q/t. Since V = IR and I = V/R we can rewrite instantaneous power in two other ways:
Topic 5.1 ExtendedB – Electric power The collisions of the electrons with the lattice structure of the resistor (or any conductor, for that matter) will cause heat to be produced. We call this thermal energy joule heat or I squared R losses. In transmission lines, joule heat is a non-desirable phenomenon. In heating elements joule heat is desirable. A heating element is rated at 1500 W when plugged into a 120 V outlet. If the heating coil breaks at one end, and you repair it by cutting off 10% of its total length, how will the power rating be affected? The resistance is proportional to the length, so the new R is equal to .9R0. = 1.11P0 = 1.11V2/R0 Since P = V2/R = V2/.9R0 then P = 1.11(1500) = 1667 W FYI: This home repair could convert a safe heater into a potentially dangerous one!
Topic 5.1 ExtendedB – Electric power Electric bills (someday you, too, will be paying them, reflect payment for electricity in units of kilowatt hours. Note that watt is a unit of power, whereas hour is a unit of time. Thus a kWh is a unit of energy. 1 kWh = (1000 W)(3600 s) = 3.6106 J How much does it cost to "run" a 150 W light bulb per day if it is on all the time and the electric company charges 15¢ per kWh? Unit cancellation is useful: 1 kW 1000 W 150 W $0.15 kW h 24 h 1 day = $0.54 per day How much energy is used up in one day by the bulb? Energy = power times time: 24 3600 s = 12,960,000 J Energy = 150 W
Topic 5.1 ExtendedB – Electric power In our society, about 30% of our electrical energy is used for lighting. FYI: This is the equivalent of about 100 power plants of 1 GW each! About 7% of our electrical energy is used by refrigerators. FYI: This is another 25 power plants! FYI: This is why the government is pushing for energy efficient refrigerators, air conditioners, dishwashers, water heaters, etc. Over 30,000,000,000 kWh of energy have been save so far.