Since we often use electricity to convey energy from one location to another, it is important to be able to quantify and calculate the rate at which energy is delivered by an electric circuit. The rate at which energy transfers from one location to another is technically referred to as power (\(P\)), and it is typically measured in the unit of the watt (1 watt = 1 joule of energy per second of time).
The total amount of power (energy per unit time) carried by an electric current is proportional to the strength of that current as well as the amount of potential (voltage) between the poles of the electrical source. Thus, power is equal to the product of current and voltage in a formula called Joules’ Law:
\[P = I V\]
Where,
\(P\) = Power in watts (joules of energy per second of time)
\(I\) = Current in amperes
\(V\) = Voltage in volts
We may prove the correctness of this formula by verifying all the units of measurement agree:
\[P = IV\]
\[[\hbox{Watts}] = [\hbox{Amperes}] \times [\hbox{Volts}] \hbox{\hskip 20pt or \hskip 20pt} [\hbox{W}] = [\hbox{A}] [\hbox{V}]\]
\[\left[\hbox{Joules} \over \hbox{Seconds} \right] = \left[\hbox{Coulombs} \over \hbox{Seconds}\right] \times \left[\hbox{Joules} \over \hbox{Coulombs}\right] \hbox{\hskip 20pt or \hskip 20pt} \left[\hbox{J} \over \hbox{s} \right] = \left[\hbox{C} \over \hbox{s} \right] \left[\hbox{J} \over \hbox{C} \right]\]
Note how the basic units for power (joules per second) are indeed equal to the product of voltage (joules per coulomb) and current (coulombs per second). This process of checking for agreement between units of measurement in a physics formula is called dimensional analysis.