 Back in the day when we talked about power we defined it more or less as the rate at which work is being done. P = Topic 5.1 Extended B – Electric power Work time  But in electricity we know that the work W in moving a charge q through a potential difference of V is given by Average Power W = qV. Thus P = qV t Average Power  If the current I and the voltage V are constant, we can write the average power as the instantaneous power like this, P = IV Instantaneous Power since I = q/t.  Since V = IR and I = V/R we can rewrite instantaneous power in two other ways: P = I 2 R P = V2RV2R FYI: Electrical power is measured in joules/second or watts, just as in mechanics.

 The collisions of the electrons with the lattice structure of the resistor (or any conductor, for that matter) will cause heat to be produced. Topic 5.1 Extended B – Electric power  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.9R 0.  Since P = V 2 /R = V 2 /.9R 0 = 1.11V 2 /R 0 = 1.11P 0 = 1667 W then P = 1.11(1500) FYI: This home repair could convert a safe heater into a potentially dangerous one!

 Electric bills (someday you, too, will be paying them, reflect payment for electricity in units of kilowatt hours. Topic 5.1 Extended B – Electric power  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) = 3.6  10 6 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: 150 W 1 kW 1000 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: Energy = 150 W  3600 s  24 = 12,960,000 J

 In our society, about 30% of our electrical energy is used for lighting. Topic 5.1 Extended B – Electric power  About 7% of our electrical energy is used by refrigerators. FYI: This is the equivalent of about 100 power plants of 1 GW each! 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.