Electrical Power and Energy
Power and energy questions in this paper usually combine a formula with a costing or efficiency calculation. Learn all three power forms and the difference between the watt and the kilowatt-hour.
The three power formulas
- P = VI
- P = I²R
- P = V²/R
All three are the same law written differently and are valid for DC and for purely resistive AC loads.
Energy and the unit
Energy W = P t. The electricity board bills energy in kilowatt-hours: 1 unit = 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J. An energy meter records kWh; a wattmeter records kW at the instant of measurement.
Heating effect
H = I²Rt joules. This is the principle of the electric heater, fuse and incandescent lamp, and it is also the source of I²R loss in machines and cables.
Efficiency
η = output/input × 100%. Input = output + losses.
Worked example
A 2000 W water heater runs 3 hours daily for 30 days. Tariff is ₹4.50 per unit. Monthly energy = 2000 × 3 × 30 = 180000 Wh = 180 kWh. Cost = 180 × 4.50 = ₹810. If the same heater takes 2.5 kWh from the mains to deliver 2.0 kWh of heat, its efficiency is 2.0/2.5 × 100 = 80%.
Traps
- Quoting energy in watts or power in kWh.
- Forgetting to divide by 1000 when converting Wh to kWh.
- Using P = VI cos φ for a DC circuit, where power factor does not exist.
- Mixing seconds and hours inside one calculation.
- Treating the fuse rating as a measure of energy.