The work done by the electric field to move a unit of electrical charge between two points in a circuit represents the potential difference between these points.
This relationship is expressed in the following equation:
ΔV = W/q
On the other hand we have, that the electric field is a conservative field; This means that the work carried out by the field, between two points, does not depend on the path followed by the electric charge between these points.
When connecting several components between two points in a circuit (parallel connection), the electric charge moves through several paths between these two points but the work performed by the field, or the potential difference between the points, is the same for all paths. So in this type of connection, the potential difference is the same for all components.
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