In parallel connections there is more than one path for the charges to follow.  A single charge will go through one of the connected elements, but not all of them, kind of like a toll plaza in Illinois.

This time the voltage across each parallel connected element is the same.  This is because the charge carriers must lose all of the energy by the time they get back to the source.  Since they only go through a single load in the circuit, all of the energy has to be dumped in that load.

Since the loads are separated more than one charge carrier can be going through the loads at the same time.  More current will flow through a parallel combination as a result.  The total current is divided among the individual loads.  This is why a parallel circuit is referred to as a current divider.

If more resistors are added to a parallel combination the circuit will allow more current to flow.  The resistance of the parallel combination decreases as more resistances are added.  To get a sum to decrease as more elements are added requires you add the inverses of the values.  This is a source of error in circuit calculations.  Most student forget they are working with inverses and do the problem incorrectly.  Use of the X^-1 button on your calculator is a big help in avoiding this.

For parallel circuits the total resistance is less than the smallest resistance in the connection.

EX.  Find the missing values in this parallel circuit

You can use the box method again for this circuit, you just have to charge the rules which govern the movement in a column.

Here is a summary of the circuit rules for the two types of electrical circuits.  Remember that all circuits, no matter what type, are a combination of these two conections.