The manufacturer of a 9 [V] flashlight battery says that the battery will deliver 20 [mA] for 80 continuous hours. However, during that time the voltage will drop from 9 [V] to 6 [V]. Assume the voltage drop is linear in time, but that the current is constant. How much energy does the batteiy deliver in 80 [h]? Battery "capacity" can be stated in terms of the total charge the battery will deliver, with units of milliamp-hours [mA-h]. If the battery can be considered "dead" when the voltage reaches 6 V, what is the capacity of the flashlight battery in mA-h?

a. Energy ≅ 43.2 kJ

b. Capacity of battery = 1600-mAh

Explanation:

average voltage value = (9 + 6)/2 = 15/2 = 7.5

current = 20 mA = 20 x

time duration = 80 hrs = 80 x 60 x 60 = 288000 sec

If the current is assumed to be constant, then the energy delivered is the product of voltage across, current delivered and the time duration during which it is delivered.

Energy delivered by battery = 7.5 x 20 x  x 288000 = 43200 J

Energy ≅ 43.2 kJ

If the battery is considered dead when it reaches 6-v, then that means that at 6-v, there is no potential difference between them.

capacity of flashlight battery is the product of current delivered and the time duration of delivery.

capacity =  20-mA x 80-hr = 1600-mAh

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