Voltage is measured in volts (joules per coulomb) and represents the potential electrical energy in each unit of charge. To add voltage simply means to place a particle at a particular place within the field of potential energy. The electric field can me measured with this formula, where E is the electric field intensity, F is the electric force and q is a positive, stationary point charge.
http://www.search.com/reference/Electric_field
Work is performed to counteract forces, and electrical fields are conservative, meaning negative work is produced. Negative work causes a decrease in the intensity of the energy level, so when a particle enters a lower level of energy, the particle's energy is decreased and extra energy is released, usually in the form of heat. This is because of thermodynamic property of entropy, or the tendency of nature to move from a state of order to one of disorder or randomness.
The First Law of Thermodynamics dictates that a change in internal energy is equal to the heat added or subtracted from a system subtracted by the work performed by the system:
W=△E
An effective way to understand the properties of thermodynamics and electrical engineering is by running a current through a resister, or series of resisters. A power source, such as a battery, creates a voltage stream of electrons within a system flowing from positive to negative. This flow of voltage passes through a resister, which absorbs power. Power in the electrical world is represented by the formula:
wikipedia.com
Oscar gave us various formulas to measure the voltage running through various elements we might use to build our circuits, such as these:
An important property of resisters is how resisters within the same electrical circuit interact. Two circuits connect in a chain, one after the other in a straight line, can be added together, so two resisters of 10 KΩ would combine to equal 20 KΩ, wheres two resisters running parallel do not and must be calculated.
Stay tuned for the exciting world of breadboard experimentation...