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Homework Help: Battery capacity and time to full discharge

  1. Feb 14, 2005 #1
    A certain car batter with a 12.0 V emf has an initial charge of 120 A*h. Assuming that the potential across the terminals stays constant until the battery is completely discharged, for how many hours can it deliver energy at the rate of 100 W?

    I am not sure how to get time in to the situaution. I know that the answer is obtained by taking (12 V * 120 A*h)/ 100 W = 14.4 hrs
  2. jcsd
  3. Feb 14, 2005 #2
    Current is the rate of the change of charge in time:
    I = Q / t.

    Power is computed (here) as product of current and potential across the terminals:
    P = I * U

    By eliminating the current I from upper equations, you get:
    t = Q / I = Q / (P / U) = Q * U / P

    charge Q = 120 Ah, U = 12 V, P = 100 W.

    t = Q * U / P = 120 Ah * 12 V / 100 W = 14.4 hrs
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