An off-grid cabin is powered by a battery bank that is recharged each day by a small…
PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity
Problem
An off-grid cabin is powered by a battery bank that is recharged each day by a small solar array. The occupants wish to know whether their current daily energy use is compatible with the average output of the solar panels.
(a) The table below lists the power ratings and daily usage times for four common devices in the cabin.
Device
Power (W)
Operating time per day (h)
LED lighting
24
5
Laptop computer
65
3
Water pump
90
0.5
Portable heater
500
1
Calculate the electrical energy used by each device in kilowatt-hours.
(b) Determine the total electrical energy consumed by the cabin per day and convert this value to megajoules.
(c) The solar array delivers an average of 4.5kWh of electrical energy to the battery bank each sunny day. Assuming one cloudy day out of every five during which the array provides only 20\% of its average output, evaluate whether the solar array supplies enough energy on a long-term average basis. Show all reasoning.
(d) If the analysis in part (c) indicates a shortfall, estimate either (i) by what factor the solar array’s average daily energy output must increase, or (ii) by how many hours the occupants must reduce the daily use of the portable heater to balance the cabin’s energy budget. Justify your answer with appropriate calculations.