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The formula for power

Like energy, we often hear the word ‘power’. In everyday life, it has many meanings but, in physics, it has a very specific meaning – it is a measure of the rate at which work is done (or similarly, at which energy is transferred).

The ability to accurately measure power was one of the key skills that allowed engineers back in the day to develop the steam engines that powered the industrial revolution. It remains crucial to understand how best to use the energy resources that power the modern world.

The power formula does not just apply to mechanical energy, but also to electricity and chemistry. The power formula also allows you to calculate thermal energy (e.g., the formula for power in electronics is the product of current and voltage - P=Ul).
The formula for power, in the case of a direct current electrical circuit, is determined using Ohm's law. The formula for power is then: P=12R or P=U2/R

Formula for power
By definition, one watt is equal to one joule of work done per second. So, if P represents power in watts, Delta E is the change in energy (number of joules), and Delta t is time in seconds, then the formula for power is:
P = ΔE/Δt

There is also another unit of power that is still widely used – horsepower. This is usually denoted by the symbol hp and has its origins in the 17th century, when it referred to the power of a typical horse used to turn a winch. Since then, horsepower has been defined as the power required to lift a 75kg mass over a distance of 1 metre in 1 second. So, how much power is that in watts?

Well, we know that when lifting against gravity, mass acquires gravitational potential energy – Ep = m⋅g⋅h.

Application of the power formula
In practice, the power formula can be used, for example, when selecting a suitable resistor for an electrical system. It can also be used to calculate whether a specific maximum power of that model is sufficient for a given project. If the calculation is wrong, a circuit component – or even the whole circuit – may be damaged. Automation, robotics, electronics are the main fields where the power formula and power information are often used. Engineering and sciences base much of their research on power.

How do we measure variable power?
In many situations where energy resources are used, the rate of consumption varies over time. One such example is typical electricity consumption in homes. We observe minimal use during the day, followed by maximum use during meal preparation and an extended period of heavy use for evening lighting and heating.

There are at least three ways of expressing power that are relevant here: instantaneous power, average power and peak power. The electricity company has to keep track of all this. In fact, different energy resources are often used to solve each of these.

- Instantaneous power is the power measured at a given moment. If you consider the power formula, P = ΔE / ΔtP, this is the measurement you get when Δt is very small. If you are lucky enough to have a power-time relationship graph, instantaneous power is simply the value you can read off the graph at any time.

- Average power is the power measured over a long period (i.e., when Δt in the power formula is very large). One way to calculate this is to find the area under the power vs. time curve (which gives the total work done) and divide it by the total time. This is usually best done using differential calculus but can often be estimated quite accurately using only geometry.

- Peak power is the maximum value that instantaneous power can have in a particular system over a long period of time. Car engines and stereo systems are examples of systems that have the ability to deliver peak power much higher than their average rated power. However, it is usually only possible to maintain this power for a short time if any damage is to be avoided. Nevertheless, in these applications, a high peak power may be more important for the driving or listening experience rather than a high average power.


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