The Actual Physics

The Arduino microcontroller is what is known as a modular circuit board. This means that instead of having fixed components in a circuit with fixed currents and voltages at every given point, different components can be attached to what are called "pins" and can be used to create completely unique circuits. However, despite the complexity gap between a simple one resistor, one voltage source circuit and the Arduino board, the physics that governs both is the same. At any given junction or node in an Arduino circuit or any circuit in general, the current that comes in is equal to the current going out (as shown in the above example circuit). This is an established law known as Kirchoff's Current Law and was first discovered through observation rather than in mathematical context. Another one of Kirchoff's Laws that is also relevant in this context is known as Kirchoff's Voltage Law and this law states that the sum of the voltages at every point in a loop is equal to 0. The last law related to these two is that of Ohm's Law, which states that the voltage at a given point is the product of the current and the resistance (V=IR). When these three laws are combined, it is possible to analyze and solve for the currents and voltages at essentially any point in the circuit. The two main types of circuit analysis are known as Nodal Analysis and Mesh Analysis and dictate the creation of any circuit, including the modular ones created using the Arduino platform.