The capacity of a storage battery such as that used in an automobile\'s electric

Question

The capacity of a storage battery such as that used in an automobile's electrical system is rated in ampere-hours (A x h) . A 50.0A x h battery can supply a current of 50.0 A for 1.00 h , or 25.0 A for 2.00 h , and so on.


Part A

What total energy can be supplied by a 12.9 V, 60A x hbattery if its internal resistance is negligible?


Part B


If a generator with an average electrical power output of 0.490 kW is connected to the battery, how much time will be required for it to charge the battery fully?

Explanation / Answer

a First of all I would like to clarify the difference between POWER and ENERGY. Power is the amount of force that a machine can supply/consume and energy is the amount of force that a machine can supply/consume or supplied/consumed for a given time. Since the question does not involve any amount of time, what we are looking for is the POWER that the battery can give and not ENERGY. The formula for Power is P=VxA, so P=15V x 60A, which amounts to 900 watts. Please note that the unit for Power is Watts and for Energy is Watt-Hours. So we can say that the battery can supply Energy to a load of 900W in 1 hour and a load of 450W in 2 hours. We will use the formula for Energy, E=P x T in this question since it asks for the amount of time. We therefore have 900W-H = 0.40kW x T; since 0.40kW = 400W, we have 900W-H = 400W x T; dividing both sides by 400 and crossing-out W, we now have 2.25 H = T. So T (time it takes to charge the battery) is equal to 2.25 H (hours).

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