In a parallel circuit, all components are connected to the same pair of nodes, which ensures that the voltage across each component is identical. This is due to the definition of parallel connections, where all points on a node maintain the same voltage level. When resistors are connected in parallel, the ends are linked by a conducting wire, preventing any voltage difference from existing. If a voltage difference were present, current would flow until equilibrium is reached, equalizing the voltage. Thus, the voltage remains constant across all components in a parallel circuit.