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 100 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.

Explanation:

Power consume by the electronic is 50W,when operated by 12V source

Power of the battery

Battery rated as 12.6V and 100ampshours

Then the power =IV

P=100×12.6

Power of battery =1260Whours

Therefore since the electronics consume 5W, then, the time taken to consume 1260Whours is

T=1260Wh/5W

T=252hours.

The energy store in the battery in KWh,

Since the P is 1256Wh

Then divide by 1000 to KW since 1KW =1000W.

Then,

E=1.256KWh

The battery cost $75

And can only be charge 300 times.

Therefore the energy that the battery can generate during it life time is 1.256×300

E=376.8KWh

This is the total energy the battery can generate before recycling

Then the cost of the battery in dollars / KWh is

$75/376.8KWh

Which is $0.199/KWh

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