Efficiency

The efficiency of a system can be calculated using either energy values or power values, as power is simply the rate of energy transfer ($P = \frac{E}{t}$).

Energy Formula: $Efficiency = \frac{\text{useful output energy transfer}}{\text{total input energy transfer}}$

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

Efficiency is expressed either as a decimal (ranging from $0$ to $1$) or as a percentage (ranging from $0\%$ to $100\%$). To convert a decimal to a percentage, multiply by $100$.

The 100% Rule: In the real world, efficiency can never be $100\%$ or greater. If your calculation results in a value over $1.0$ or $100\%$, you have likely swapped the input and output values in your formula.

Unit Consistency: Ensure that both the numerator and denominator use the same units (e.g., both in $kJ$ or both in $W$). Efficiency itself must never have a unit attached to the final numerical answer.

Multi-Step Problems: Often, you must calculate the useful output first (e.g., using $\Delta E_p = mgh$ for a crane) before you can find the efficiency. Always identify the 'intended purpose' to find the useful energy.

Contextual Improvements: When asked how to improve efficiency, be specific to the scenario. Don't just say 'reduce waste'; specify 'lubricate joints' for a bike or 'add insulation' for a heating system.

'Lost' vs 'Wasted': Energy is never truly 'lost' due to the Law of Conservation of Energy; it is only transferred into non-useful stores. Use the term dissipated to describe energy spreading into the surroundings.

Decimal vs Percentage: Students often forget to multiply by $100$ when a percentage is requested, or they accidentally multiply by $100$ twice. Always check if the question asks for a 'ratio' or a 'percentage'.

Power vs Energy Confusion: While both can be used to find efficiency, do not mix them in the same fraction. You cannot divide useful power by total energy.