Power and energy in everyday systems
📖Definition— Definitions
- Energy (E) — measured in joules (J). 1 J = energy to lift 1 N a distance of 1 m.
- Power (P) — rate of energy transfer, measured in watts (W). 1 W = 1 J/s.
Key equations
P = E / t — power = energy transferred ÷ time taken.
E = P × t — useful for calculating energy use of an appliance.
P = I × V — electrical power = current × potential difference (an alternative.)
✦Worked example— Worked examples
A 2 kW kettle runs for 3 minutes: E = P × t = 2000 × 180 = 360 000 J = 360 kJ.
A toaster transfers 90 000 J in 60 s: P = E / t = 90 000 / 60 = 1500 W = 1.5 kW.
A hairdryer rated 230 V, 8.7 A: P = I × V = 8.7 × 230 ≈ 2000 W.
Energy bills — kilowatt-hours (kWh)
Domestic energy is sold by the kWh: energy used by a 1 kW appliance for 1 hour. 1 kWh = 3.6 × 10⁶ J.
Cost = power (kW) × time (h) × price per kWh.
Power in the National Grid
The National Grid distributes electricity from power stations to homes:
power station → step-up transformer → high-voltage transmission → step-down transformer → consumers.
P = IV — for a fixed power, raising V lowers I. Lower current → less heat dissipated in cables (P = I²R losses) → higher efficiency.
Efficiency
efficiency = (useful energy out / total energy in) × 100%
A typical lamp: 15% useful (light), 85% wasted (heat). LEDs reach 80–90% useful.
OCR exam tip
When the question asks "calculate the energy used by a 0.8 kW appliance for 30 minutes", convert to base units first: 0.8 kW = 800 W; 30 min = 1800 s. E = 800 × 1800 = 1 440 000 J. Skipping conversion is the most common 0/3.
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