Power describes how quickly energy is transferred or work is done. Two machines can do the same amount of work, but the one that finishes in less time has greater power. This idea matters in engines, electric motors, appliances, sports, and any system where speed of energy transfer affects performance.
The SI unit of power is the watt, where 1 watt equals 1 joule per second.
In a real machine, input energy is split into useful output energy and wasted energy such as heat, sound, or vibration. Efficiency compares the useful output to the total input and is usually written as a percentage. Mechanical power often comes from force and velocity, while electrical power often comes from voltage and current.
These formulas let you compare devices, predict energy use, and explain why no real machine is 100 percent efficient.
Understanding Physics: Power and Efficiency
Power is often confused with energy because both describe what a system can do. Energy is the total amount available or transferred. Power tells you how fast that transfer happens.
A battery can store a large amount of energy yet deliver it slowly. A small motor can run for a long time with little power. A powerful motor can transfer energy quickly, but it may empty its energy source sooner.
This difference explains why power ratings matter for kettles, heaters, drills, lifts, and electric vehicles. A higher power appliance usually does its task faster, though it can use more electrical energy if it runs for the same length of time.
For moving objects, power depends on both the force applied and the speed of motion. Mechanical power equals force times velocity when the force acts in the direction of travel. A cyclist climbing a hill needs force to overcome gravity.
Pedalling faster while maintaining that force requires more power. The same idea applies to cranes lifting loads. Lifting a heavy box slowly may need modest power, while lifting it quickly needs greater power.
This is why engines have power limits. If an engine cannot provide enough power, a vehicle slows down on a steep hill even if its tyres still have enough grip.
Electrical devices have a power rating that helps predict their energy use. Electrical power equals current times voltage. At a fixed mains voltage, a device that draws more current has greater power.
A two thousand watt heater transfers energy much faster than a ten watt LED lamp. The heater is not automatically better. It is designed to produce heat, while the lamp is designed to produce light.
To find the energy used by an appliance, multiply its power by the time it operates. Electricity bills commonly use kilowatt hours. One kilowatt hour is the energy transferred by a one thousand watt device running for one hour.
Efficiency is about where the input energy goes. Friction in bearings, air resistance, electrical resistance, vibration, and unwanted sound can all reduce useful output. A machine can have high power but poor efficiency if much of its input becomes unwanted heating.
Lubrication can reduce friction. Insulation can reduce heat loss. Streamlined shapes can reduce air resistance.
Students should state clearly what counts as useful output in each situation. For a motor lifting a load, gravitational potential energy gained by the load is useful.
For a lamp, visible light is useful, while heating is usually waste. Efficiency has no unit and cannot exceed one hundred percent because a machine cannot produce more useful energy than it receives.
Key Facts
- Power is the rate of doing work: P = W / t
- The SI unit of power is the watt: 1 W = 1 J/s
- Work done by a constant force in the direction of motion is W = Fd
- Mechanical power at constant speed can be written as P = Fv
- Electrical power in a circuit is P = IV, where I is current and V is voltage
- Efficiency = useful output energy / input energy × 100%
Vocabulary
- Power
- Power is the rate at which work is done or energy is transferred.
- Work
- Work is energy transferred when a force moves an object through a distance in the direction of the force.
- Watt
- A watt is the SI unit of power and equals one joule of energy transferred each second.
- Efficiency
- Efficiency is the fraction or percentage of input energy that becomes useful output energy.
- Wasted energy
- Wasted energy is energy transferred to forms that are not useful for the intended task, such as heat or sound.
Common Mistakes to Avoid
- Confusing power with work is wrong because work is the total energy transferred, while power tells how fast that transfer happens.
- Forgetting to convert minutes to seconds is wrong because watts use joules per second, so time must be in seconds when using P = W / t.
- Using total output instead of useful output in efficiency is wrong because efficiency only counts the energy that performs the intended task.
- Writing efficiency greater than 100 percent is wrong for a real machine because some input energy is always dissipated as heat, sound, or other waste.
Practice Questions
- 1 A motor lifts a 300 N weight through a height of 2.0 m in 4.0 s. Calculate the work done and the average power output.
- 2 An electric device uses 1200 J of electrical energy and produces 900 J of useful mechanical energy. Calculate its efficiency as a percentage.
- 3 Two motors lift the same crate to the same height, but motor A takes 5 s and motor B takes 10 s. Explain which motor has greater power and whether they do the same amount of work.