A home uses a 1.8 kW heater for 2.5 h, six 9 W lamps for 5.0 h, and a 120 W refrigerator for an effective 8.0 h daily. Solar supplies 6.2 kWh through a battery of 82% round-trip efficiency. (a) Find each and total demand. (b) Find useful battery energy and grid shortfall. (c) Convert demand to joules. (d) At 230 V find heater current and choose 3, 5, 10 or 13 A fuse. (e) Explain two reasons this balance does not prove off-grid operation.

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Demand 5.73 kWh; battery output 5.084 kWh; shortfall 0.646 kWh; 2.06 × 10⁷ J; heater current 7.83 A, choose 10 A. Heater uses 1.8 × 2.5 = 4.50 kWh. Lamps total 54 W = 0.054 kW and use 0.270 kWh. Refrigerator uses 0.120 × 8.0 = 0.960 kWh. Total = 4.50 + 0.270 + 0.960 = 5.73 kWh. Battery delivers 0.82 × 6.2 = 5.084 kWh, leaving 0.646 kWh from grid. Using 1 kWh = 3.6 × 10⁶ J, demand = 5.73 × 3.6 × 10⁶ = 2.06 × 10⁷ J. Heater current = 1800/230 = 7.83 A. The smallest listed fuse above normal current is 10 A; a 5 A fuse would interrupt normal use. Daily totals omit timing, battery capacity and peak power. Weather, state of charge, inverter loss and appliance starting currents can prevent off-grid operation despite an average energy balance.

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