Question

A battery takes 2.0MJ to charge. If the charger operates using 40.0 W but it is only 90% efficient, how long does it take to charge?

The answer in the textbook is 56s but an explanation would be helpful. Thanks!

Answer 1

The time is `=5.610^4s`, See the explanation

Explanation:

Energy necessary to charge the battery is `E=2*10^6J`

Power of charger is `P=40W`

Efficiency of charger is `eta=90%`

Power used effectively to charge the battery is

`P_e=40*90/100=36W`

Let the time taken to charge the battery be `=ts`

Then,

`E=P_e*t`

The time is

`t=E/P_e=(2*10^6)/(36)=5.610^4s`

The answer is different from `56s`

It would be `=56s` only if `E=2.0kJ`