Final answer:
Kirchhoff's first rule, also known as the junction rule, states that the current in the main line of a parallel circuit equals the sum of the individual branch currents due to charge conservation.
Step-by-step explanation:
Kirchhoff's Junction Rule in Parallel Circuits
The law that states the current in the main line of a parallel circuit equals the sum of the individual branch currents is known as Kirchhoff's first rule or the junction rule. According to this rule, the sum of all currents entering a junction must equal the sum of all currents leaving the junction. This is due to the conservation of charge principle, which means that charge is neither created nor destroyed at the junction.
The junction rule can be succinctly written as Σ Iin = Σ Iout, where 'I' represents the current. For instance, if a circuit splits into two branches after a junction, with branch currents I1 and I2, and the total current before the split is I, then Kirchhoff's junction rule dictates that I = I1 + I2. This rule is fundamental when analyzing current flow in parallel circuits.