Question

The rate at which a battery charges is slower the closer the battery is to its maximum charge Co. The time (in hours) required to charge a fully discharged battery to a charge

C is given by
t = -k in(1-C/C0)
where k is a positive constant that depends on the battery. For a certain battery, k = 0.25. If this battery is fully discharged, how long will it take to charge to 40% of its maximum charge Co? (Round your answer to three decimal places.)
____hr

Answer 1

The time required to charge a fully discharged battery to a certain charge can be calculated using the equation t = -k ln(1-C/C0), where t is the time in hours, k is a positive constant, C is the desired charge, and C0 is the maximum charge. For a certain battery with k = 0.25, it will take approximately 0.169 hours, or 10.14 minutes, to charge the battery to 40% of its maximum charge.

Step-by-step explanation:

The time required to charge a fully discharged battery to a charge C is given by the equation t = -k ln(1-C/C0), where t is the time in hours, k is a positive constant, C is the desired charge, and C0 is the maximum charge.

In this case, we are given that k = 0.25 and we want to charge the battery to 40% of its maximum charge (C = 0.40C0).

Plugging in these values into the equation, we get t = -0.25 ln(1-0.40) = -0.25 ln(0.60) ≈ 0.169 hours.

Therefore, it will take approximately 0.169 hours, or 10.14 minutes, to charge the battery to 40% of its maximum charge.