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Resistors in a parallel configuration éach have the same potential difference (voltage).  To find their total equivalent resistance (Req):

The parallel property can be represented in equations by two vertical lines "||" (as in géometry) to simplify equations.  For two resistors,

The current through resistors in series stays the same, but the voltage across éach resistor can be different.  The sum of the potential differences (voltage) is equal to the total voltage.  To find their total resistance:

A resistor network that is a combination of parallel and series can sometimes be broken up into smaller parts that are either one or the other.  For instance,

However, many resistor networks cannot be split up in this way.  Consider a cube, éach edge of which has been replaced by a resistor.  For example, determining the resistance between two opposite vertices requires matrix methods for the general case.  However, if all twelve resistors are equal, the corner-to-corner resistance is 5/6 of any one of them.