30. The electronics aboard a certain sailboat consume 50 W when operated from a

Question

30. The electronics aboard a certain sailboat consume 50 W when operated from a 12.6-V source. If a certain fully charged deep-cycle lead acid storage battery is rated for 12.6 V and 100 ampere hours, for how many hours can the electronics be operated from the battery without recharging? (The ampere- hour rating of the battery is the operating time to discharge the battery multiplied by the current.) How much energy in kilowatt hours is initially stored in the battery? If the battery costs $75 and has a life of 300 charge- discharge cycles, what is the cost of the energy in dollars per kilowatt hour? Neglect the cost of recharging the battery.

Explanation / Answer

Given Voltage of Battery Vb = 12.6 V

Ah rating of battery = 100

Energy stored in battery Eb = 100*12.6 = 1260 Wh

Operating Voltage of Sail Boat VL = 12.6 V

Power required by Load PL = 50 W

Completely Charged battery will supply power to load for time T = 1260 / 50 = 25.2 Hours

Cost of battery C = $ 75

Battery stores Eb = 1.26 kWh / cycle

No.of Cycles of operation of battery N = 300 charge cycle

Energy stored for 300 cycles ET = 300*1.26 = 378 kWh

Cost of energy per kWh = 75 / 378 = $ 0.198 / kWh

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