If the resistors are connected in series, the total resistance is equal to the sum of the individual resistances i.e.:
RTotal = R1 + R2 + ... + Rn
Series resistors are often used as voltage dividers to provide a reference voltage of a fixed percentage of the supply voltage. Below is an interactive example.
⚠ The application of these circuits requires careful consideration as the load can affect the effective resistance of the part of the divider that it is connected across - see parallel resistors.
If resistors are connected in parallel, the total resistance is equal to the inverse of the sum of the inverse of the individual resistances i.e.:
⅟RTotal = ⅟R1 + ⅟R2 + ... + ⅟Rn
Parallel resistors are often used to obtain non-preffered resistance values i.e. where a value is required that cannot be bought off the shelf or as current dividers (shunts). Parallel resistance calculations also come into play when you introduce a load across part of a voltage divider. Below is an interactive example.
Resistor Bridges are generally used for measurement circuits for example Wheatstone Bridge circuits. Normally one of the resistors would be replaced with a device such as a thermistor or light dependant resistor. They combine series and parallel resistances.