The rate at which a battery charges is slower the closer the

The rate at which a battery charges is slower the closer the battery is to Its maximum charge C_0. The time (In hours) required to charge a fully discharged battery to a charge C is given by t = -k ln (1 - C/c_0) 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 C_0? ()

Solution

given t =-k ln(1 - C_/Co)

given k =0.25,

C =40% of maximum charge C_o

=>C=0.4C_o

t =-0.25 ln(1 - 0.4Co_/Co)

t =-0.25 ln(1 - 0.4)

t =-0.25 ln(0.6)

t=0.128 hr

it will take 0.128 hr for the battery to charge 40% of its maximum charge C_o