Ohm's Law is limited in certain electric circuits due to its assumption of constant resistance, which does not hold in non-linear components or at varying temperatures. The loop rule, derived from the conservation of energy, explains that the total voltage around a closed loop must equal zero, emphasizing energy conservation in circuits. The relationship between branch points and independent currents is governed by Kirchhoff's laws, which state that the sum of currents entering a junction equals the sum leaving it. This analogy can be visualized using water flow in pipes, where resistance affects the distribution of current. Understanding these concepts is crucial for effectively analyzing complex circuits.