Final answer:
The current through each branch circuit in a parallel circuit depends on the resistance of each branch, following Ohm's Law and Kirchhoff's junction rule.
Step-by-step explanation:
Given a constant supply, the current through each branch circuit in a parallel circuit depends on the resistance of each branch. In a parallel circuit, each resistor has the same voltage of the source applied to it, but the current flowing through each resistor is different. According to Ohm's Law (I = V/R), where I is the current, V is the voltage, and R is the resistance, the current in each branch can be calculated by dividing the voltage by the resistance of that particular branch. Therefore, resistors with lower resistance will have a higher current flowing through them, and those with higher resistance will have a lesser current flow. Moreover, the total current supplied by the source is the sum of the currents through each resistor as per Kirchhoff's junction rule, which states that the sum of the currents entering a junction must equal the sum of the currents leaving the junction.