Power - Definition
Power is a measure of the work done per unit time. Many actions may require the same quantity of work to complete, such as people of equal mass going up the same flight of stairs. However, the time in which each person completes the task determines that person's power. The person who gets to the top of the stairs in the least amount of time has the greatest power. The SI unit for power is the watt (W), and it is equivalent to a joule second-1 or J/s. Power can be calculated by dividing the work done by the time taken to complete the work. Therefore, P = W/t.
Power - Circuits
When people think of power, they may think of the electricity that is used in their home. Power is not a measure of current, but current (a flow of charges) must be moved through a circuit when work is applied. In fact, the work that is done to move charges along a circuit is referred to as voltage. Current and voltage collectively are used to describe electrical power. Earlier, it was noted that power is work done per unit time. Analysis of units for current and voltage shows how the formula for electrical power is different than that given above, which is useful for mechanics only.
Voltage is a measure of the work done of charges, indeed a volt can be expressed as a joule per coulomb. Recall that current is measured in amperes, and an ampere is equivalent to coulombs per second. Both of these units contain coulomb because they each deal with charge, however for voltage it is in the numerator and for current it is in the denominator. The product of these units gives joules per second, the unit for power. Therefore electrical power is the product of current and voltage.
When performing circuit analysis, power is additive, regardless of whether the cirucit is series or parallel.
In order to determine how much power is generated by a hydroelectric dam, it's necessary to review some principles of work and energy. Recall that work can causes conversions between different types of energy, and in the case of falling water from a dam, there is a conversion from potential to kinetic energy. The kinetic energy of the water can be used to turn a turbine, and from there electricity can be generated. If 100% efficiency is assumed, and for simplicity it is here, the formula for power can be altered accordingly:
Since g is a constant and h represents the vertical distance the water falls, those variables are easy substitutions. Determining the mass of water that falls over the dam each second is another matter entirely. It's not particularly plausible to know the mass of water that falls over the dam each second, but the volume of water per second is viable. Since density relates mass and volume, the following substitution can be made: