Definition of Power

Power is a physical quantity that conveys the rate of energy conversion or transfer. It’s the amount of energy consumed or produced per unit time.
In classical mechanics, it is often defined as the rate at which work is done. The SI unit of power is the watt (W), which is equivalent to a joule of work per second (J/s).
In mathematical notation, power (P) is defined as the work done (W) over the time (t) it took for the work to be done: P = W/t.
If the work done (W) is defined as the force (F) multiplied by the distance (d) that the force is applied along, we get an alternative form of the power formula: P = F * (d/t). Here, D/t can also represent velocity (v), hence an alternative form: P = F * v.
Power can also be defined in terms of rotational mechanics. For a rotating object, power is then the product of the angle (Ω) at which the force is applied and the torque (τ) it produces: P = τ * Ω.
Power is a scalar quantity, meaning it only has magnitude and no direction.
Power is also a time derivative of energy, so it’s obtained as the energy’s rate of change with respect to time: P = dE/dt.

Types of Power

Instantaneous Power: This denotes the rate at which work is being done at any given moment. It’s the limit of the average power as the time duration approaches zero, expressed mathematically as: P = lim (ΔW/ Δt) as Δt → 0. Here, ΔW is the work done in the infinitesimal time interval Δt.
Average Power: This denotes the total work done divided by the total time it took. It provides the average rate of energy transfer over a defined period of time: P_avg = W_total/t_total.

Power is predominantly used to calculate the efficiency of energy conversions and transfers, which are significant in engineering, physics, and various industrial applications.
Understanding power is critical when designing and analysing engines, power supplies, electrical circuits, and other machinery where energy transfer or conversion is involved.
In physics, the concept of power is utilized to determine the amount of work done by a force over a certain period of time, which proves important when studying energy, force, and kinematics.
The concepts of average and instantaneous power are widely used in electricity generation and distribution, structural and mechanical engineering, and telecommunications among many other fields.