Efficiency and Power

Efficiency measures how much of the input energy (or power) is usefully transferred.

$\boxed{\text{Efficiency} = \frac{\text{useful output energy}}{\text{total input energy}}}$

Or equivalently:

$\text{Efficiency} = \frac{\text{useful output power}}{\text{total input power}}$

Efficiency can be expressed as a decimal (e.g., 0.75) or a percentage (e.g., 75%).

To convert: multiply the decimal by 100.

Key Points

• Efficiency is always less than 1 (or less than 100%) — you can never get more useful energy out than you put in
• Wasted energy = input energy − useful output energy
• The wasted energy usually goes to thermal energy stores (heating surroundings)

Typical Efficiencies

To improve efficiency:

• Lubrication — reduces friction between moving parts, less energy wasted as heat
• Streamlining — reduces air resistance/drag
• Insulation — reduces heat loss (e.g., in homes, engines)
• Better design — e.g., LED bulbs instead of filament bulbs
• Regenerative braking — converts kinetic energy back to electrical energy (electric cars)

Power is the rate at which energy is transferred (or work is done).

$\boxed{P = \frac{E}{t}}$

Where:

• $P$ = power (in watts, W)
• $E$ = energy transferred (in joules, J)
• $t$ = time (in seconds, s)

1 watt = 1 joule per second (1 W = 1 J/s)

Larger Units

• 1 kilowatt (kW) = 1000 W
• 1 megawatt (MW) = 1,000,000 W

Also: $P = F \times v$ (power = force × velocity) — useful for moving objects.

Rearranging

$E = P \times t \qquad t = \frac{E}{P}$

Electricity bills use kilowatt-hours instead of joules:

$\text{Energy (kWh)} = \text{Power (kW)} \times \text{Time (hours)}$

Converting: 1 kWh = $1000 \times 3600 = 3{,}600{,}000$ J = 3.6 MJ

$\text{Cost} = \text{Energy (kWh)} \times \text{Price per kWh}$

• Efficiency = useful output ÷ total input (as decimal or percentage)
• Efficiency is always < 1 (< 100%); wasted energy usually becomes heat
• Power = energy ÷ time: $P = E/t$ (watts)
• 1 kWh = energy from 1 kW for 1 hour = 3.6 MJ
• Cost = energy (kWh) × price per kWh
• Reduce waste: lubrication, insulation, streamlining, better technology