Power

What is Power?

In general, the term power is applied to provide an indication of how much work (energy conversion) can be accomplished in a specified amount of time; that is, power is a rate of doing work.
For instance, a large motor has more power than a smaller motor because it has the ability to convert more electrical energy into mechanical energy in the same period of time. Since energy is measured in joules (J) and time in seconds (s), power is measured in joules/second (J/s).
The electrical unit of measurement for power is the watt (W), defined by
$$ \text{1 watt (W)} = \text{1 joule/sec}$$ In equation form, power is determined by $$ P = {W \over t} $$ with the energy (W) measured in joules and the time t in seconds.
James Watt
The unit of measurement - the watt - is derived from the surname of James Watt. Who was instrumental in establishing the standards for power measurements. He introduced the horsepower (hp) as a measure of the average power of a strong dray horse over a full working day. It is approximately 50% more than can be expected from the average horse. The horsepower and watt are related in the following manner: $$\text{1 horsepower} = \text{746 watts} $$ The power delivered to, or absorbed by, an electrical device or system can be found in terms of the current and voltage by, $$ P = {W \over t} = {QV \over t} = V {Q \over t}$$ but $$ I = Q/t $$ so that, $$ \bbox[5px,border:1px solid red] {\color{blue}{P = VI}} $$ By direct substitution of Ohm's law, the equation for power can be obtained in two other forms: $$ P = VI = V ({V \over R})$$ $$ \bbox[5px,border:1px solid red] {\color{blue}{P = {V^2 \over R}}} \text{ (watts,W)}$$ Or $$ P = VI = (IR) I $$ $$ \bbox[5px,border:1px solid red] {\color{blue}{P = I^2 R }} \text{ (watts,W)}$$
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