HW1_solutions - ECE 333 Homework 1 Solutions Spring 2010...

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ECE 333 Homework 1 Solutions :: Spring 2010 1.6 A 52-gallon electric water heater is designed to deliver 4800 W to an electric resistance heating element in the tank when it is supplied with 240 V (it doesn't matter if this is ac or dc). a. What is the resistance of the heating element? P ! V 2 R ! R ! V 2 P R ! 240 2 " V # 4800 " W # $ R ! 12 "%# b. How many watts would be delivered if the element is supplied with 208 V instead of 240 V? P ! V 2 R P ! 208 2 " V # 12 "%# $ P ! 3605.33 " W # c. Neglecting any losses from the tank, how long would it take for 4800 W to heat the 52 gallons of water from 60 o F to 120 o F? The conversion between kilowatts of electricity and Btu/hr of heat is given by 3412 Btu/hr = 1 kW. Also, one Btu heats 1 lb of water by 1 o F and 1 gallon of water weighs 8.34 lbs. & T ! 120 o ' 60 o ! 60 o F 52 gal of H 2 O $ 52 ( 8.34 ! 433.68 lbs 3412 Btu ) hr 1 kW ( 4.8 kW ! 16377.6 Btu ) hr 1 hr 16377 Btu ( 1 Btu 1 lb 1 o F ( 60 o F ( 433.68 lbs ! 1.589 hr 1.7 Suppose an automobile batter is modeled as an ideal 12-V battery in series with an internal resistance of 0.01 ! as shown in Figure P1.7 (pg. 46 Masters) [1].
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