*The key difference between power and energy is that power is the rate at which energy is used or transferred, measured in watts (W) while, energy is the total capacity to do work, measured in joules (J).*

**What is Power?**

Power is defined as the rate at which energy is transferred or converted over time. In the International System of Units (SI), power is measured in watts, where one watt equals one joule per second. Power is a scalar quantity.

When discussing power in specific systems, other related factors must be considered. For instance, the power needed to move a ground vehicle is calculated as the sum of the aerodynamic drag and the traction force applied to the wheels, multiplied by the vehicle’s velocity. In the case of a motor, the output power is determined by the product of the torque the motor produces and the angular velocity of its output shaft. Similarly, the power dissipated by an electrical component in a circuit is the product of the current passing through the component and the voltage across it.

Power is the capacity to resist external forces.

Power is the capability to affect or influence others.

Power involves having control or authority over something or someone.

Power is the ability to tackle challenging tasks.

**Calculating Power:**

**General Formula:**Power (P) = Work / Time**Standard Electric Power Formula:**Power = Voltage × Current**Electric Power in Resistors:**Power = I²R, where ‘I’ is the current and ‘R’ is the resistance.

**What is Energy?**

Power measures the rate at which energy is used or transferred. It is calculated as the amount of energy divided by the time it takes to use that energy. The unit of power is the watt, which represents one joule of energy used per second. For example, a circular saw requires a specific amount of power to operate, and the rate at which power is drawn from a battery affects how long the stored energy lasts.

The formula for power is:

P=ΔEsysΔtP = \frac{\Delta E_{\text{sys}}}{\Delta t}P=ΔtΔEsys

where:

- PPP is the average power output, measured in watts (W),
- ΔEsys\Delta E_{\text{sys}}ΔEsys is the net change in the system’s energy in joules (J), also known as work,
- Δt\Delta tΔt is the time duration, measured in seconds (s).

Multiplying power by the duration of its use gives the amount of energy consumed. This explains why a kilowatt is a unit of power, while a kilowatt-hour (1 kilowatt over 1 hour) is a unit of energy.

Tasks, such as lifting a box, require a specific amount of energy (in joules). However, completing the task more quickly (with a smaller Δt\Delta tΔt) necessitates more power (measured in watts).

**Calculating Energy:**

**Kinetic Energy:**K.E = ½ mv², where ‘m’ is the mass of the object and ‘v’ is its velocity.**Potential Energy:**P.E = mgh, where ‘m’ is the mass, ‘g’ is the acceleration due to gravity, and ‘h’ is the height of the object.

**Power vs Energy**

The primary differences between power and energy are given below:

Aspect | Power | Energy |

Definition | The rate at which energy is used or transferred. | The capacity to do work or the amount of work done. |

Formula | P=ΔEsysΔtP = \frac{\Delta E_{\text{sys}}}{\Delta t}P=ΔtΔEsys. | Depends on context (e.g., E=P×tE = P \times tE=P×t for electrical energy). |

Units | Watts (W). | Joules (J). |

Measurement | Amount of energy per unit time. | Total amount of work done or energy stored. |

Time Dependence | Power is time-dependent (energy per second). | Energy is not inherently time-dependent. |

Examples | Power of a light bulb, power output of an engine. | Energy stored in a battery, kinetic energy of a moving object. |

Relation | Energy divided by time. | Power multiplied by time. |