Final answer:
Having only one pair of connecting leads in parallel circuits ensures that the current is the same at every point in the circuit. Each resistor in parallel draws the same current it would if it were alone connected to the voltage source.
Step-by-step explanation:
The advantage of having only one pair of connecting leads to the source for all the parallel branches is that the current is the same at every point in the circuit. This is because there is only one path for current to flow. Each resistor in parallel draws the same current it would if it were alone connected to the voltage source. For example, in a power distribution system, parallel connections are used to supply various devices with the same voltage and allow them to operate independently.