Why is voltage the same in a parallel circuit

[ehabmozart]

I am wondering why are voltages the same across a parallel circuit. How can we say that it depends on the start and end points only. On what basis? Thanks for clarifying!

 

[Dale]

By definition. All elements which are in parallel are connected to the same pair of nodes (definition of parallel) and all points on a given node are at the same voltage (definition of node).

 

[phyzguy]

Consider two resistors in parallel. The ends of the resistors are connected together with a conducting wire. Good conductors cannot support a voltage difference, because if there is any voltage difference, current flows until the voltage is the same.