A 23 V battery powers a 316 load for 26 hours If the Ah effi

A 23 V battery powers a 316 load for 2.6 hours.

If the A-h efficiency of the battery is 0.88, and the battery charger provides 105 mA of current, determine the time it will take to charge the battery in hours.

Assume that the battery voltage remains constant over the discharge period

please show full working out

Solution

output of battery is (v^2)/R

23^2/316=1.678 watts

energy=power*time

1.678*2.6=4.352 watt-hour (discharing enrgy)

now battery charing 105ma with efficincy 0.88

out put current is 105*0.88

92.4 ma

power=92.4ma*23v=2.1252 w

energ is same

2.1252*t(charing)=4.352 watt hour

charging=2.04 hour