Ohm's law defines the most important relationship between resistors and other components in a DC circuit. You use resistors to control the current and voltage at different points in a circuit. In its equation format, Ohm's law is voltage (V) = current (I) times resistance (R). Algebraically we can convert this to I = V/R or R = V/I. They all represent the relationship between V, I, and R. A practical exercise would be to hook a 12K resistor across a 12 volt battery. If we want to see how much current this circuit is pulling from the battery, we solve for I. The equation would be I = the voltage V (12volts) divided by the resistance R (1200ohms). I = 12/1200 or .01 amps (10milliamps).
If we wanted to have 14K ohms across the same battery, we could add a 2K resistor in "series" where the current would flow through them serially. The formula to calculate resistors in series is R(T) = R(1) + R(2) + R(3). You simply add all the resistances together to get the total resistance. It is often necessary to use multiple resistors in series to obtain different voltages that the circuit requires. In series resistors, the total resistance will always be larger than the largest individual resistor.
Using resistors in parallel means connecting the resistors side-by-side rather than serially. Reference 2 below includes diagrams that will help you visualize the difference between parallel and series. The formula for calculating the total resistance of resistors in parallel is 1/R(T) = 1/R(1) + 1/R(2) + 1/R(3). In parallel resistor networks, the total resistance will always be smaller than the smallest individual resistor in the parallel array.
Resistors have power ratings based on their resistance and current handling capability. When you use resistors in series, you need to calculate the current flow through each resistor to determine the power handling capability required. Generally, the larger the physical size of the resistor, the larger its wattage. It would not be unusual for a series resistor group to have resistors with different power ratings.
While carbon composition resistors count for the majority of resistors used, there are several other types that deserve mention. Wire-wound resistors are generally reserved for high current handling capability. They are obvious because of their larger size and they usually have a ceramic case. Fusible resistors are designed to be a resistor under normal circumstances but act as a fuse when the circuit draws excess current. Metal film resistors are common in high-frequency equipment.