• Parallel

The potential difference across each resistor is the same, but the currents through them are typically different, where I = I₁ + I₂ + I₃.  This lead to the equivalent resistance formula,

Note that both of the diagrams below represent resistors in parallel.

                            

• Combinations

Some circuits can be analysed as combinations of series and parallel circuits. In the circuit below R₂ and R₃ are in parallel, their equivalent resistance is then in series with R₁.

Note that it is not possible to represent all circuits as combinations of series and parallel elements, this is most obvious in many cases where there is more than one battery in the circuit, see example below.  To analyse this type of circuit we must use Kirchhoff's Laws.