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Getting Power from Voltage and Current

  1. Jan 26, 2014 #1
    1. The problem statement, all variables and given/known data
    A constant current of 3 A for 4 hours is required to charge an automotive
    battery, and the battery's terminal voltage is v(t) = 10 + t/2 V, where t is in hours.
    Assuming an electricity cost $0.12 per KWh, what is the cost to charge the battery?

    2. Relevant equations
    p(t) = i(t)v(t)


    3. The attempt at a solution
    So I just thought that I could multiply current (3A) with the voltage (10 + 4h/2)V and get power in watts, which would be 36W. I divide 36 by 1000, 0.036kW, and then I multiply that by the cost ($0.12/kWh) to get some number/h, and then multiply that number by 4 hours to get the cost to charge the battery. However, this isn't giving me the right answer, I would greatly appreciate it if someone could point me in the right direction. Thank you.
     
  2. jcsd
  3. Jan 26, 2014 #2

    SteamKing

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    The electricity cost is metered by the total amount of energy charged into the battery (Notice: the price of electricity is $0.12 per kilowatt-hour).

    You have a changing voltage as the battery charges but a constant current input. What would be the total energy required to charge the battery according to the info in the OP?
     
  4. Jan 26, 2014 #3
    Well, I know that energy is the integral of p(t), so would I take the integral with the lower limit being 0 and upper limit being 4, and then multiply that number by the cost of electricity?
     
  5. Jan 26, 2014 #4

    SteamKing

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  6. Jan 26, 2014 #5
    Alright, thanks alot for your help. Just to clarify, I took $0.012/kWh, multiplied it by 1kWh/3600000J, and then I got $number/J, and then I calculated for the amount of joules using the integral of my power equation, substituting in 4 for time, and multiplied that number by the price of electricity/joules.
     
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