The effects of open circuits:

An open circuit is essentially a break in the circuit. An open circuit in a series circuit will prevent the flow of current through the circuit. With no current flowing in the circuit there can be no voltage drop across any resistors, and therefore the supply potential will be measured at all points between the positive terminal and the break.
 
In a circuit with parallel paths, an open circuit path will cause an increase in the circuit resistance and a reduction in the circuit current. The change in current flow will cause the voltages measured around the circuit to change.