Power

Power and its Measurements

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

  • Measured in watts (W) in the International System of Units (SI).
  • One watt is equal to one joule of energy transferred or work done per second (1 W = 1 J/s).
  • Power can also be expressed in kilowatts (kW), where 1 kW = 1000 W.

Mathematical Relationships of Power

  • Calculation of Power can be done using the formula:
    • Power (P) = work done (W) / time taken (t)
    • This can also be expressed as: P = ΔE / t, where ΔE is the change in energy.
  • When force (F) is moving an object at a constant velocity (v), the formula transforms into:
    • P = F * v
    • This formula shows that power also depends on the speed at which the work is done.
  • If the force and distance are known, power can also be calculated using the formula:
    • P = Force (F) x distance (d) / time (t)

Power in Electrical Systems

  • In the context of electrical systems, power (P) is given by the formula:
    • P = voltage (V) x current (I)
    • Power can also be calculated using an alternative formula, known as Joule’s law, expressed as: P = I²R, where I is the current and R is the resistance.

Power Transfers and Efficiency

  • Power transferred or transformed in a process can be split into useful power output and wasted power.

  • The efficiency of a device or process can be calculated using the ratio of useful power output to total power input, usually expressed as a percentage.

  • Efficiency = (useful power output / total power input) x 100%

  • In reality, no process can be 100% efficient as always some power ends up wasted, most commonly as heat due to friction or resistance.

Power Consumption

  • Power ratings of electrical appliances indicate the rate at which they convert electrical energy into another form of energy (usually heat, sound, or light).

  • For instance, a 60 W light bulb transforms 60 J of electrical energy into light and heat energy every second.

  • Monitoring and controlling power consumption is important for managing energy resources and reducing our environmental impact.

Power and Sustainability

  • Choosing appliances with lower power ratings and using energy more efficiently can help to reduce power consumption and contribute to sustainability.