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Example 17.6 The Cost of Lighting Up Your Life Goal Apply the electric power concepts, and calculate the cost of power usage using kilowatt-hours. Problem A circuit provides a maximum current of 24.4 A at an operating voltage of 1.20 x 102 V. (a) How many 75 W bulbs can operate with this voltage source? (b) At $0.110 per kilowatt-hour, how much does it cost to operate these bulbs for 8.97 h? Strategy Find the necessary power with 9' = IAV, then divide by 75.0 W per bulb to get the total number of bulbs. To find the cost, convert power to kilowatts and multiply by the number of hours, then multiply by the cost per kilowatt-hour. Solution (a) Find the number of bulbs that can be lighted. Substitute into Equation 17.8 to get the total 37: = my = (24_4 A)(1.20 x 102 V) = 2_93 x 103 w power. Divide the total power by the power per bulb , I l l ' to get the number of bulbs. Bum "3r \"f 111th = ll )1] 1' Number of bulbs = :] \"total = m 75.0 W (b) Calculate the cost of this electricity for an 8.97 h day. 1.00 x 1\"" Vi: Find the energy in kilowatt-hours. Energy = Pr = (2.92:3 x 103 W) ( ) (8.9? 11) Energy = 26.2 kWh Multiply the cost per kilowatt-hour. Cost = [26.2 kWhil$0.11/kWh) Cost = $ Remarks The amount of energy might correspond to what a small office uses in a working day, taking into account all power requirements (notjust lighting). In general, resistive devices can have variable power output, depending on how the circuit is wired. Here, power outputs were specified, so such considerations were unnecessary. Hints: Getting Started | I'm Stuck ' (a) How many Christmas tree lights drawing 5.00 W of power each could be run on a circuit operating at 1.20 x 102 V and providing 16.0 A of current? (b) Find the cost to operate one such string 24.0 h per day for the Christmas season (two weeks), using the rate $0.11/kWh. $:l 2. [l1 Points] DETAILS SERCP7 17.P.001. If a current of 89.0 mA exists in a metal wire, how many electrons ow past a given cross section of the wire in 11.5 minutes? Sketch the direction of the current and the direction of the electrons' motion. (Do this on paper. Your instructor may ask you to turn in your work.) 3. [11 Points] DETAILS SERCP7 17.P.015.SOLN. A potential difference of 14 V is found to produce a current of 0.44 A in a 3.7 m length of wire with a uniform radius of 0.41 cm. Find the following values for the wire. (a) the resistance 9 (b) the resistivity 4. [-11 Points] DETAILS SERCP7 17.P.031.SOLN. A toaster is rated at 650 W when connected to a 90 V source. What current does the toaster carry, and what is its resistance? :] A 52 5. [-11 Points] DETAILS SERCP7 17.P.032. If electrical energy costs 12 cents, or $0.12, per kilowatt-hour, then what would the following events cost? (a) Burn a 60 W light bulb for 24 h straight. $:] (b) Operate an electric oven for 4.0 h if it carries a current of 20.0 A at 220 V. $:] 6. [-I1 Points] SERCP7 17.P.036. The power supplied to a typical black-and-white television set is 86 W when the set is connected to 120 V. (a) How much electrical energy does this set consume in 1 hour? :P (b) A color television set draws about 2.2 A when connected to 120 V. How much time is required for it to consume the same energy as the black-and-white model consumes in 1 hour? Em How many 109 W lightbulbs can you use in a 132 V circuit without tripping a 16 A circuit breaker? (The bulbs are connected in parallel, which means that the potential difference across each lightbulb is 132 V.) A high-voltage transmission line with a resistance of 0.28 SZ/km carries a current of1030 A. The line is at a potential of 670 W at the power station and carries the current to a city located 159 km from the station. (a) What is the power loss due to resistance in the line? :]W (b) What fraction of the transmitted power does this loss represent