You and a friend are studying late at night. There are three 150 W light bulbs a

Question

You and a friend are studying late at night. There are three 150 W light bulbs and a radio with an internal resistance of 44.0 plugged into the living room electrical outlets. You decide to have a break and have a snack, turning on the pop-corn machine that draws 6.00 A. How much electrical power are you using? Data: Assume the electric company provide you with 110 V potential difference.

All the electrical outlets are part of the same 110-V circuit which has a 10-A circuit breaker. How much current in amperes (A) is required to feed all the devices described above? This tells you if you should or should not turn on the pop-corn machine.  

You are so tired after studying that you leave all of these household devices turned on for 13.0 hours. Calculate the cost (in dollars) of the electric bill, if the commercial rate is $.09/kWh? (Do not enter units)  

Explanation / Answer

V = potential difference = 110 Volts

Pr = total power by the bulbs = 150 x 3 = 450 Watt

Pradio = power by the radio = V2/R = 1102/44 = 275 watt

Pm = power by the machine = iV = 6 x 110 = 660 watt

Total power is given as
Ptotal = Pr + Pradio + Pm = 450 + 275 + 660 = 1385 Watt

ibulb = current to each bulb = P/V = 150/110 = 1.4 A

iradio = Pradio/V = 275/110 = 2.5 A

imachine = 6 A

so total current drawn = itotal = ibulb +  iradio + imachine = 1.4 + 2.5 + 6 = 9.9 A

energy consumed = Ptotal t = 1385 x 13 = 18.005 kWh

Cost = Rate x energy consumed = 0.09 x 18.005 = $1.62

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