Resistors
Resistors are electronic and electric components that oppose the flow of current in a circuit. They are made from relatively poor conductors but that don't stop current from flowing altogether.
There are many kinds of resistor constructions, each suited for many purposes that overlap.
The simplest form is a cylinder of carbon material with two connection leads attached at both sides. The diameter and length of the cylinder, as well as the carbon composition of the filling determine the resistance. In general, a longer cylinder has more resistance than a shorter one, and a thicker one will have less resistance than a thin cylinder.
The apparent counter intuitive nature of a thick resistor having less resistance lies in how current flows in a circuit: it will always look for an easier path, and with a thick resistor with more overlapping paths, current has a higher chance of finding an easier path than in a limited and crowded thin resistor.
Another construction method is to coat a ceramic core with a resistor material and shape it in the form of a spiral by removing some of the material along the edge of the spiral. Since this method effectively increases or decreases the length of the resistor material, resistance can be carefully selected and determined.
High power resistances use that same method but instead of resistor material covering a core, resistive wire is used to allow for better heat handling.
Resistors have a standard color code that reflects the value of the resistance of the component. It consists of four color bands, the first two represent numbers and the third represents the number of zeros to add at the end of such number (more on the color code).
Series and parallel resistors
Series when only two components, in this case resistors, share only one of their connections; It could also be described as connecting one resistor after the other forming a chain.
From the construction characteristics of resistors, we can see that when we connect resistors in series, we are effectively creating a single, longer resistor, so what happens with the total resistance?
Simple, they are added together.
For example, we have a square tube we will fill with water. If we wanted to know the volume, we multiply base times height of the water in it to get the volume of water we put in. We measure separately the volume of a one by one cube of water and another of one by two, and get 1 and 2 respectively. We then fill tube with both, how much volume is the water in the tube?
We only put in 3 units of volume, and if we know that none leaked out of the tube, there can be no less than 3 units. So in effect the volumes add together.
Now the volume can be thought as the resistance, put two resistors into a single line and their resistances add up. No math involved, although there's a math proof of this derived from ohm's law.
Parallel is when two or more components share both of their connections together.
What happens with the resistance in parallel circuits? It happens something similar as having a thicker resistor, but not for the same reasons.
Imagine a circuit with one voltage source and two resistors in parallel, both resistors draw current from the source. From the point of view of the source, providing more current to the circuit is the same as providing current to a lower valued resistance, following I = V/R. To know exactly how much resistance the source 'sees' we have to do some math.
It = V/R1 + V/R2 : where It is the total current supplied by the source, R1 and R2 the respective resistances.
V/Rt = V/R1 + V/R2 : We replace It with V/Rt, since we want to know the total resistance the source 'sees'
1/Rt = 1/R1 + 1/R2 : Divide both sides by V
From this last formula we see that the inverse of the resistance is what's added thogether. The formula can be further worked to result in a simple, easy to remember formula.
1/Rt = (R1+R2)/(R1*R2)
Rt = (R1*R2)/(R1+R2)
Note that this only works for two resistors.
