Question

Our 12 V car battery does not appear to be functioning correctly, so we measure the voltage with a volt meter and find that the voltage on the battery is only 9V. To fix the problem, we connect the battery to a charger which delivers a constant current of i = 15 A. After t = 53 min on the charger, we find that voltage on the car battery is now 12.6V. Assuming that the voltage changed linearly during the charging process, how much energy was delivered to the car battery.

Answer 1

Answer:

 507599.78 J

Explanation:

Charge input = current x time

=15 x 53 x 60

= 47000 coulomb

increase in voltage

= 12.6 - 9 = 3.6

capacity of the battery C = Charge input / increase in voltage

= 47000 / 3.6 = 13055.55

energy of the capacitor = 1/2 CV²

Initial energy of car battery =  .5 x 13055.55 x 9 x 9

= 528749.77 J

Final energy of car battery

= .5 x 13055.55 x 12.6 x 12.6

= 1036349.55

Increase in energy = 507599.78 J