Question

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.

Answer 1

Answer:

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