The electronics aboard a certain sailboat consume 50 W whenoperated from 12.6-V source. If a certain fully charged deep-cyclelead acid storage battery is rated for 12.6 V and 300 ampere hours, for how many hours can the electronics be operated from the batterywithout recharging. (The ampere-hour rating of the battery is theoperating time to discharge the battery multiplied by the current.) How much energy in Kilowatt hours is initially stored in thebattery? If the battery costs $75 and has a life 0f 300charge-discharge cycle, what is the cost of the energy in dollarsper kilowatt hour? Neglect the cost of recharging the battery.

The energy stored in a battery is 3.78 KWhr

The time of operation of a battery on a single charge is 75.6 hrs

The cost of energy is $ 0.066/KWhr

Explanation:

First, we find the energy stored in battery:

Energy = (Voltage) (Ampere Hour Rating)

Energy = E = (12.6 V) (300 Ahr)

E = 3780 Whr = 3.78 KWhr

Now, for the time of operation:

Time of operation = t = Energy/Power

t = 3780 Whr/50W

t = 75.6 hrs

Now, for the cost of energy:

Cost = Cost of Battery/Total energy of battery

Total energy of battery = (Total charge-discharge Cycles) (Energy of 1 cycle)

Total energy = (300 cycles) (3.78 KWhr/cycle)

Total Energy = 1134 KWhr

Therefore,

Cost = $ 75/1134 KWhr

Cost = $ 0.066/KWhr